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Solution
Q.1 Correct
Q.1 In-correct
Q.1 Unattempt

Four particles each of mass 1kg are placed at four corners of a square of side 2m. Moment of inertia of system about an axis perpendicular to its plane and passing through one of its vertex is____ kgm2.

[27-Jan-2024 Shift 1]

Four particles each of mass 1kg are placed at four corners of a square of side 2m. Moment of inertia of system about an axis perpendicular to its plane and passing through one of its vertex is____ kgm2.

[27-Jan-2024 Shift 1]
Q.2 Correct
Q.2 In-correct
Q.2 Unattempt

A ring and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of both bodies are identical and the ratio of their kinetic energies is 7/x where x is

[27-Jan-2024 Shift 2]

A ring and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of both bodies are identical and the ratio of their kinetic energies is 7/x where x is

[27-Jan-2024 Shift 2]
Q.3 Correct
Q.3 In-correct
Q.3 Unattempt

A body of mass 5kg moving with a uniform speed 3√2ms−1 in X − Y plane along the line y = x + 4. The angular momentum of the particle about the origin will be ____kgm2 s−1.

[29-Jan-2024 Shift 2]

A body of mass 5kg moving with a uniform speed 3√2ms−1 in X − Y plane along the line y = x + 4. The angular momentum of the particle about the origin will be ____kgm2 s−1.

[29-Jan-2024 Shift 2]
Q.4 Correct
Q.4 In-correct
Q.4 Unattempt

Consider a Disc of mass 5kg, radius 2m, rotating with angular velocity of 10rad∕ s about an axis perpendicular to the plane of rotation. An identical disc is kept gently over the rotating disc along the same axis. The energy dissipated so that both the discs continue to rotate together without slipping is______ J.

[30-Jan-2024 Shift 1]

Consider a Disc of mass 5kg, radius 2m, rotating with angular velocity of 10rad∕ s about an axis perpendicular to the plane of rotation. An identical disc is kept gently over the rotating disc along the same axis. The energy dissipated so that both the discs continue to rotate together without slipping is______ J.

[30-Jan-2024 Shift 1]
Q.5 Correct
Q.5 In-correct
Q.5 Unattempt

Two discs of moment of inertia I1 = 4kgm2 and I2 = 2kgm2 about their central axes & normal to their planes, rotating with angular speeds 10rad∕ s & 4rad∕ s respectively are brought into contact face to face with their axe of rotation coincident. The loss in kinetic energy of the system in the process is ______J.

[30-Jan-2024 Shift 2]

Two discs of moment of inertia I1 = 4kgm2 and I2 = 2kgm2 about their central axes & normal to their planes, rotating with angular speeds 10rad∕ s & 4rad∕ s respectively are brought into contact face to face with their axe of rotation coincident. The loss in kinetic energy of the system in the process is ______J.

[30-Jan-2024 Shift 2]
Q.6 Correct
Q.6 In-correct
Q.6 Unattempt

Two identical spheres each of mass 2kg and radius 50cm are fixed at the ends of a light rod so that the separation between the centers is 150cm. Then, moment of inertia of the system about an axis perpendicular to the rod and passing through its middle point is x/20 kg m2, where the value of x is___

[31-Jan-2024 Shift 2]

Two identical spheres each of mass 2kg and radius 50cm are fixed at the ends of a light rod so that the separation between the centers is 150cm. Then, moment of inertia of the system about an axis perpendicular to the rod and passing through its middle point is x/20 kg m2, where the value of x is___

[31-Jan-2024 Shift 2]
Q.7 Correct
Q.7 In-correct
Q.7 Unattempt

A cylinder is rolling down on an inclined plane of inclination 60∘. It's acceleration during rolling down will be  where x =______ (use g = 10m∕ s2).

[29-Jan-2024 Shift 1]

A cylinder is rolling down on an inclined plane of inclination 60∘. It's acceleration during rolling down will be  where x =______ (use g = 10m∕ s2).

[29-Jan-2024 Shift 1]
Q.8 Correct
Q.8 In-correct
Q.8 Unattempt

A body of mass ' m ' is projected with a speed ' u ' making an angle of 45∘ with the ground. The angular momentum of the body about the point of projection, at the highest point is expressed as  The value of ' X ' is______

[31-Jan-2024 Shift 2]

A body of mass ' m ' is projected with a speed ' u ' making an angle of 45∘ with the ground. The angular momentum of the body about the point of projection, at the highest point is expressed as  The value of ' X ' is______

[31-Jan-2024 Shift 2]
Q.9 Correct
Q.9 In-correct
Q.9 Unattempt

A ball of mass 0.5kg is attached to a string of length 50cm. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is 400N. The maximum possible value of angular velocity of the ball in rad∕ s is,:

[1-Feb-2024 Shift 1]

A ball of mass 0.5kg is attached to a string of length 50cm. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is 400N. The maximum possible value of angular velocity of the ball in rad∕ s is,:

[1-Feb-2024 Shift 1]
Q.10 Correct
Q.10 In-correct
Q.10 Unattempt

A disc of radius R and mass M is rolling horizontally without slipping with speed v. It then moves up an inclined smooth surface as shown in figure. The maximum height that the disc can go up the incline is :

[1-Feb-2024 Shift 2]

A disc of radius R and mass M is rolling horizontally without slipping with speed v. It then moves up an inclined smooth surface as shown in figure. The maximum height that the disc can go up the incline is :

[1-Feb-2024 Shift 2]
Q.11 Correct
Q.11 In-correct
Q.11 Unattempt
Solid sphere A is rotating about an axis PQ. If the radius of the sphere is 5‌cm then its radius of gyration about PQ will be √x‌cm. The value of x is___

[24-Jan-2023 Shift 1]
Solid sphere A is rotating about an axis PQ. If the radius of the sphere is 5‌cm then its radius of gyration about PQ will be √x‌cm. The value of x is___

[24-Jan-2023 Shift 1]
Q.12 Correct
Q.12 In-correct
Q.12 Unattempt
A uniform solid cylinder with radius R and length L has moment of inertia I1, about the axis of cylinder. A concentric solid cylinder of radius R′=‌
R
2
 and length L′=‌
L
2
 is caned out of the original cylinder. If I2 is the moment of inertia of the carved out portion ot the cylinder then ‌
I1
I2
=___
[24-Jan-2023 Shift 2]
A uniform solid cylinder with radius R and length L has moment of inertia I1, about the axis of cylinder. A concentric solid cylinder of radius R′=‌
R
2
 and length L′=‌
L
2
 is caned out of the original cylinder. If I2 is the moment of inertia of the carved out portion ot the cylinder then ‌
I1
I2
=___
[24-Jan-2023 Shift 2]
Q.13 Correct
Q.13 In-correct
Q.13 Unattempt
A car is moving with a constant speed of 20 m∕ s in a circular horizontal track of radius 40 m. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be : (Take g=10 m∕ s2)
[25-Jan-2023 Shift 1]
A car is moving with a constant speed of 20 m∕ s in a circular horizontal track of radius 40 m. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be : (Take g=10 m∕ s2)
[25-Jan-2023 Shift 1]
Q.14 Correct
Q.14 In-correct
Q.14 Unattempt
An object of mass 8‌kg is hanging from one end of a uniform rod CD of mass 2‌kg and length 1m pivoted at its end C on a vertical wall as shown in figure. It is supported by a cable AB such that the system is in equilibrium. The tension in the cable is :
(Take g=10m∕ s2 )

[25-Jan-2023 Shift 1]
An object of mass 8‌kg is hanging from one end of a uniform rod CD of mass 2‌kg and length 1m pivoted at its end C on a vertical wall as shown in figure. It is supported by a cable AB such that the system is in equilibrium. The tension in the cable is :
(Take g=10m∕ s2 )

[25-Jan-2023 Shift 1]
Q.15 Correct
Q.15 In-correct
Q.15 Unattempt
ICM is moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc. IAB is it's moment of inertia about an axis AB perpendicular to plane and parallel to axis CM at a distance ‌2∕3R from center. Where R is the radius of the disc. The ratio of IAB and ICM is x:9. The value of x is ________.

[25-Jan-2023 Shift 1]
ICM is moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc. IAB is it's moment of inertia about an axis AB perpendicular to plane and parallel to axis CM at a distance ‌2∕3R from center. Where R is the radius of the disc. The ratio of IAB and ICM is x:9. The value of x is ________.

[25-Jan-2023 Shift 1]
Q.16 Correct
Q.16 In-correct
Q.16 Unattempt
If a solid sphere of mass 5‌kg and a disc of mass 4 kg have the same radius. Then the ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be ‌
x
7
. The value of x is ______.
[25-Jan-2023 Shift 2]
If a solid sphere of mass 5‌kg and a disc of mass 4 kg have the same radius. Then the ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be ‌
x
7
. The value of x is ______.
[25-Jan-2023 Shift 2]
Q.17 Correct
Q.17 In-correct
Q.17 Unattempt
A car is moving on a horizontal curved road with radius 50m. The approximate maximum speed of car will be, if friction between tyres and road is 0.34. [. Take g=10ms−2]
[29-Jan-2023 Shift 1]
A car is moving on a horizontal curved road with radius 50m. The approximate maximum speed of car will be, if friction between tyres and road is 0.34. [. Take g=10ms−2]
[29-Jan-2023 Shift 1]
Q.18 Correct
Q.18 In-correct
Q.18 Unattempt
A solid sphere of mass 2‌kg is making pure rolling on a horizontal surface with kinetic energy 2240J. The velocity of centre of mass of the sphere will be _______ ms−1.
[29-Jan-2023 Shift 1]
A solid sphere of mass 2‌kg is making pure rolling on a horizontal surface with kinetic energy 2240J. The velocity of centre of mass of the sphere will be _______ ms−1.
[29-Jan-2023 Shift 1]
Q.19 Correct
Q.19 In-correct
Q.19 Unattempt
An object moves at a constant speed along a circular path in a horizontal plane with centre at the origin. When the object is at x=+2m, its velocity is −4‌
^
j
m∕ s. The object's velocity (v) and acceleration (a) at x=−2m will be
[29-Jan-2023 Shift 2]
An object moves at a constant speed along a circular path in a horizontal plane with centre at the origin. When the object is at x=+2m, its velocity is −4‌
^
j
m∕ s. The object's velocity (v) and acceleration (a) at x=−2m will be
[29-Jan-2023 Shift 2]
Q.20 Correct
Q.20 In-correct
Q.20 Unattempt
A car is moving on a circular path of radius 600m such that the magnitudes of the tangential acceleration and centripetal acceleration are equal. The time taken by the car to complete first quarter of revolution, if it is moving with an initial speed of 54‌km∕hr is t(1−e−π∕2) s. The value of t is _______ .
[29-Jan-2023 Shift 2]
A car is moving on a circular path of radius 600m such that the magnitudes of the tangential acceleration and centripetal acceleration are equal. The time taken by the car to complete first quarter of revolution, if it is moving with an initial speed of 54‌km∕hr is t(1−e−π∕2) s. The value of t is _______ .
[29-Jan-2023 Shift 2]
Q.21 Correct
Q.21 In-correct
Q.21 Unattempt
A thin uniform rod of length 2m. cross sectional area ' A ' and density ' d ' is rotated about an axis passing through the centre and perpendicular to its length with angular velocity ω. If value of ω in terms of its rotational kinetic energy E is √‌
αE
Ad
 then the value of α is ________.
[30-Jan-2023 Shift 1]
A thin uniform rod of length 2m. cross sectional area ' A ' and density ' d ' is rotated about an axis passing through the centre and perpendicular to its length with angular velocity ω. If value of ω in terms of its rotational kinetic energy E is √‌
αE
Ad
 then the value of α is ________.
[30-Jan-2023 Shift 1]
Q.22 Correct
Q.22 In-correct
Q.22 Unattempt
A uniform disc of mass 0.5‌kg and radius r is projected with velocity 18m∕ s at t=0 s on a rough horizontal surface. It starts off with a purely sliding motion at t=0 s. After 2 s it acquires a purely rolling motion (see figure). The total kinetic energy of the disc after 2 s will be _______ J.
(given, coefficient of friction is 0.3 and g=10m∕ s2)

[30-Jan-2023 Shift 2]
A uniform disc of mass 0.5‌kg and radius r is projected with velocity 18m∕ s at t=0 s on a rough horizontal surface. It starts off with a purely sliding motion at t=0 s. After 2 s it acquires a purely rolling motion (see figure). The total kinetic energy of the disc after 2 s will be _______ J.
(given, coefficient of friction is 0.3 and g=10m∕ s2)

[30-Jan-2023 Shift 2]
Q.23 Correct
Q.23 In-correct
Q.23 Unattempt
Two discs of same mass and different radii are made of different materials such that their thicknesses are 1‌cm and 0.5‌cm respectively. The densities of materials are in the ratio 3:5. The moment of inertia of these discs respectively about their diameters will be in the ratio of −. The value of x is _______.
[31-Jan-2023 Shift 2]
Two discs of same mass and different radii are made of different materials such that their thicknesses are 1‌cm and 0.5‌cm respectively. The densities of materials are in the ratio 3:5. The moment of inertia of these discs respectively about their diameters will be in the ratio of −. The value of x is _______.
[31-Jan-2023 Shift 2]
Q.24 Correct
Q.24 In-correct
Q.24 Unattempt
Moment of inertia of a dise of mass M and radius ' R ' about any of its diameter is ‌
MR2
4
. The moment of inertia of this disc about an axis normal to the disc and passing through a point on its edge will be, ‌
x
2
MR2. The value of x is ______.
[1-Feb-2023 Shift 2]
Moment of inertia of a dise of mass M and radius ' R ' about any of its diameter is ‌
MR2
4
. The moment of inertia of this disc about an axis normal to the disc and passing through a point on its edge will be, ‌
x
2
MR2. The value of x is ______.
[1-Feb-2023 Shift 2]
Q.25 Correct
Q.25 In-correct
Q.25 Unattempt
A solid cylinder is released from rest from the top of an inclined plane of inclination 30∘ and length 60‌cm. If the cylinder rolls without slipping, its speed upon reaching the bottom of the inclined plane is ________ ms−1. (Given g=10ms−2 )

[1-Feb-2023 Shift 1]
A solid cylinder is released from rest from the top of an inclined plane of inclination 30∘ and length 60‌cm. If the cylinder rolls without slipping, its speed upon reaching the bottom of the inclined plane is ________ ms−1. (Given g=10ms−2 )

[1-Feb-2023 Shift 1]
Q.26 Correct
Q.26 In-correct
Q.26 Unattempt
Two identical solid spheres each of mass 2‌kg and radii 10‌cm are fixed at the ends of a light rod. The separation between the centres of the spheres is 40‌cm. The moment of inertia of the system about an axis perpendicular to the rod passing through its middle point is _______ ×10−3‌kg−m2
[6-Apr-2023 shift 1]
Two identical solid spheres each of mass 2‌kg and radii 10‌cm are fixed at the ends of a light rod. The separation between the centres of the spheres is 40‌cm. The moment of inertia of the system about an axis perpendicular to the rod passing through its middle point is _______ ×10−3‌kg−m2
[6-Apr-2023 shift 1]
Q.27 Correct
Q.27 In-correct
Q.27 Unattempt
A ring and a solid sphere rotating about an axis passing trough their centers have same radii of gyration. The axis of rotation is perpendicular to plane of ring. The ratio of radius of ring to that of sphere is √‌
2
x
. The value of x is _______.
[6-Apr-2023 shift 2]
A ring and a solid sphere rotating about an axis passing trough their centers have same radii of gyration. The axis of rotation is perpendicular to plane of ring. The ratio of radius of ring to that of sphere is √‌
2
x
. The value of x is _______.
[6-Apr-2023 shift 2]
Q.28 Correct
Q.28 In-correct
Q.28 Unattempt
The moment of inertia of a semicircular ring about an axis, passing through the center and perpendicular to the plane of ring, is ‌
1
x
MR2, where R is the radius and M is the mass of the semicircular ring. The value of x will be _______.
[8-Apr-2023 shift 1]
The moment of inertia of a semicircular ring about an axis, passing through the center and perpendicular to the plane of ring, is ‌
1
x
MR2, where R is the radius and M is the mass of the semicircular ring. The value of x will be _______.
[8-Apr-2023 shift 1]
Q.29 Correct
Q.29 In-correct
Q.29 Unattempt
A force of −P
^
k
 acts on the origin of the coordinate system. The torque about the point (2,−3) is P(
^
a
^
i
+bj), The ratio of ‌
a
b
 is ‌
x
2
. The value of x is _______.
[10-Apr-2023 shift 2]
A force of −P
^
k
 acts on the origin of the coordinate system. The torque about the point (2,−3) is P(
^
a
^
i
+bj), The ratio of ‌
a
b
 is ‌
x
2
. The value of x is _______.
[10-Apr-2023 shift 2]
Q.30 Correct
Q.30 In-correct
Q.30 Unattempt
A solid sphere of mass 500g and radius 5‌cm is rotated about one of its diameter with angular speed of 10‌rad s−1. If the moment of inertia of the sphere about its tangent is x×10−2 times its angular momentum about the diameter. Then the value of x will be ________.
[11-Apr-2023 shift 1]
A solid sphere of mass 500g and radius 5‌cm is rotated about one of its diameter with angular speed of 10‌rad s−1. If the moment of inertia of the sphere about its tangent is x×10−2 times its angular momentum about the diameter. Then the value of x will be ________.
[11-Apr-2023 shift 1]
Q.31 Correct
Q.31 In-correct
Q.31 Unattempt
A circular plate is rotating horizontal plane, about an axis passing through its center perpendicular to the plate, with an angular velocity ω. A person sits at the center having two dumbbells in his hands. When he stretches out his hands, the moment of inertia of the system becomes triple. If E be the initial Kinetic energy of the system, then final Kinetic energy will be ‌
E
x
. The value of x is ______
[11-Apr-2023 shift 2]
A circular plate is rotating horizontal plane, about an axis passing through its center perpendicular to the plate, with an angular velocity ω. A person sits at the center having two dumbbells in his hands. When he stretches out his hands, the moment of inertia of the system becomes triple. If E be the initial Kinetic energy of the system, then final Kinetic energy will be ‌
E
x
. The value of x is ______
[11-Apr-2023 shift 2]
Q.32 Correct
Q.32 In-correct
Q.32 Unattempt
For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is ‌
x
5
. The value of x is ______.
[12-Apr-2023 shift 1]
For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is ‌
x
5
. The value of x is ______.
[12-Apr-2023 shift 1]
Q.33 Correct
Q.33 In-correct
Q.33 Unattempt
A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of rotation of the sphere to the total energy of moving sphere is π:22 the, the value of its angular speed will be rad∕ s.
[13-Apr-2023 shift 1]
A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of rotation of the sphere to the total energy of moving sphere is π:22 the, the value of its angular speed will be rad∕ s.
[13-Apr-2023 shift 1]
Q.34 Correct
Q.34 In-correct
Q.34 Unattempt
A light rope is wound around a hollow cylinder of mass 5‌kg and radius 70‌cm. The rope is pulled with a force of 52.5N. The angular acceleration of the cylinder will be _______ rads−2.
[13-Apr-2023 shift 2]
A light rope is wound around a hollow cylinder of mass 5‌kg and radius 70‌cm. The rope is pulled with a force of 52.5N. The angular acceleration of the cylinder will be _______ rads−2.
[13-Apr-2023 shift 2]
Q.35 Correct
Q.35 In-correct
Q.35 Unattempt
A solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping. The ratio of their radius of gyrations respectively (k sph:keyl) is 2:√x. The value of x is _______.
[15-Apr-2023 shift 1]
A solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping. The ratio of their radius of gyrations respectively (k sph:keyl) is 2:√x. The value of x is _______.
[15-Apr-2023 shift 1]
Q.36 Correct
Q.36 In-correct
Q.36 Unattempt
A metre scale is balanced on a knife edge at its centre. When two coins, each of mass 10g are put one on the top of the other at the 10.0‌cm mark the scale is found to be balanced at 40.0‌cm mark. The mass of the metre scale is found to be x×10−2‌kg. The value of x is__
[24-Jun-2022-Shift-1]
A metre scale is balanced on a knife edge at its centre. When two coins, each of mass 10g are put one on the top of the other at the 10.0‌cm mark the scale is found to be balanced at 40.0‌cm mark. The mass of the metre scale is found to be x×10−2‌kg. The value of x is__
[24-Jun-2022-Shift-1]
Q.37 Correct
Q.37 In-correct
Q.37 Unattempt
A fly wheel is accelerated uniformly from rest and rotates through 5 rad in the first second. The angle rotated by the fly wheel in the next second, will be:
[24-Jun-2022-Shift-2]
A fly wheel is accelerated uniformly from rest and rotates through 5 rad in the first second. The angle rotated by the fly wheel in the next second, will be:
[24-Jun-2022-Shift-2]
Q.38 Correct
Q.38 In-correct
Q.38 Unattempt
If force
→
F
=3
∧
i
+4
∧
j
−2
∧
k
 acts on a particle position vector 2
∧
i
+
∧
j
+2
∧
k
 then, the torque about the origin will be :
[25-Jun-2022-Shift-1]
If force
→
F
=3
∧
i
+4
∧
j
−2
∧
k
 acts on a particle position vector 2
∧
i
+
∧
j
+2
∧
k
 then, the torque about the origin will be :
[25-Jun-2022-Shift-1]
Q.39 Correct
Q.39 In-correct
Q.39 Unattempt
Moment of Inertia (M.I.) of four bodies having same mass 'M' and radius ' 2R′ are as follows:
I1= M.I. of solid sphere about its diameter
I2= M.I. of solid cylinder about its axis
I3= M.I. of solid circular disc about its diameter
I4= M.I. of thin circular ring about its diameter
If 2(I2+I3)+I4=x.I1, then the value of x will be
[25-Jun-2022-Shift-2]
Moment of Inertia (M.I.) of four bodies having same mass 'M' and radius ' 2R′ are as follows:
I1= M.I. of solid sphere about its diameter
I2= M.I. of solid cylinder about its axis
I3= M.I. of solid circular disc about its diameter
I4= M.I. of thin circular ring about its diameter
If 2(I2+I3)+I4=x.I1, then the value of x will be
[25-Jun-2022-Shift-2]
Q.40 Correct
Q.40 In-correct
Q.40 Unattempt
A thin circular ring of mass M and radius R is rotating with a constant angular velocity 2 rads ‌−1 in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two objects each of mass m be attached gently to the opposite ends of a diameter of ring, the ring will then rotate with an angular velocity (in rads ‌−1 ).
[26-Jun-2022-Shift-1]
A thin circular ring of mass M and radius R is rotating with a constant angular velocity 2 rads ‌−1 in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two objects each of mass m be attached gently to the opposite ends of a diameter of ring, the ring will then rotate with an angular velocity (in rads ‌−1 ).
[26-Jun-2022-Shift-1]
Q.41 Correct
Q.41 In-correct
Q.41 Unattempt
A solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is
[26-Jun-2022-Shift-2]
A solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is
[26-Jun-2022-Shift-2]
Q.42 Correct
Q.42 In-correct
Q.42 Unattempt
Choose the correct answer from the options given below :

[28-Jun-2022-Shift-1]
Choose the correct answer from the options given below :

[28-Jun-2022-Shift-1]
Q.43 Correct
Q.43 In-correct
Q.43 Unattempt
A √34m long ladder weighing 10‌kg leans on a frictionless wall. Its feet rest on the floor 3m away from the wall as shown in the figure. If Ef and Fw are the reaction forces of the floor and the wall, then ratio of Fw∕Ff will be :
(Use g=10m∕s2.)

[28-Jun-2022-Shift-2]
A √34m long ladder weighing 10‌kg leans on a frictionless wall. Its feet rest on the floor 3m away from the wall as shown in the figure. If Ef and Fw are the reaction forces of the floor and the wall, then ratio of Fw∕Ff will be :
(Use g=10m∕s2.)

[28-Jun-2022-Shift-2]
Q.44 Correct
Q.44 In-correct
Q.44 Unattempt
A uniform disc with mass M=4‌kg and radius R=10‌cm is mounted on a fixed horizontal axle as shown in figure. A block with mass m=2‌kg hangs from a massless cord that is wrapped around the rim of the disc. During the fall of the block, the cord does not slip and there is no friction at the axle. The tension in the cord is ____N.
(. Take .g=10ms−2)

[28-Jun-2022-Shift-2]
A uniform disc with mass M=4‌kg and radius R=10‌cm is mounted on a fixed horizontal axle as shown in figure. A block with mass m=2‌kg hangs from a massless cord that is wrapped around the rim of the disc. During the fall of the block, the cord does not slip and there is no friction at the axle. The tension in the cord is ____N.
(. Take .g=10ms−2)

 [28-Jun-2022-Shift-2]
Q.45 Correct
Q.45 In-correct
Q.45 Unattempt
A spherical shell of 1‌kg mass and radius R is rolling with angular speed ω on horizontal plane (as shown in figure). The magnitude of angular momentum of the shell about the origin 0 is ‌
a
3
R2ω. The value of a will be:

[29-Jun-2022-Shift-1]
A spherical shell of 1‌kg mass and radius R is rolling with angular speed ω on horizontal plane (as shown in figure). The magnitude of angular momentum of the shell about the origin 0 is ‌
a
3
R2ω. The value of a will be:

[29-Jun-2022-Shift-1]
Q.46 Correct
Q.46 In-correct
Q.46 Unattempt
The moment of inertia of a uniform thin rod about a perpendicular axis passing through one end is I1. The same rod is bent into a ring and its moment of inertia about a diameter is I2. If ‌
I1
I2
 is ‌
xπ2
3
, then the value of x will be___
[29-Jun-2022-Shift-2]
The moment of inertia of a uniform thin rod about a perpendicular axis passing through one end is I1. The same rod is bent into a ring and its moment of inertia about a diameter is I2. If ‌
I1
I2
 is ‌
xπ2
3
, then the value of x will be___
[29-Jun-2022-Shift-2]
Q.47 Correct
Q.47 In-correct
Q.47 Unattempt
A solid cylinder and a solid sphere, having same mass M and radius Rv roll down the same inclined plane from top without slipping. They start from rest. The ratio of velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be :
[25-Jul-2022-Shift-1]
A solid cylinder and a solid sphere, having same mass M and radius Rv roll down the same inclined plane from top without slipping. They start from rest. The ratio of velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be :
[25-Jul-2022-Shift-1]
Q.48 Correct
Q.48 In-correct
Q.48 Unattempt
A disc of mass 1‌kg and radius R is free to rotate about a horizontal axis passing through its centre and perpendicular to the plane of disc. A body of same mass as that of disc is fixed at the highest point of the disc. Now the system is released, when the body comes to the lowest position, its angular speed will be 4√‌
x
3R
‌rad‌s−1 where x= ________. (g=10ms−2)
[26-Jul-2022-Shift-1]
A disc of mass 1‌kg and radius R is free to rotate about a horizontal axis passing through its centre and perpendicular to the plane of disc. A body of same mass as that of disc is fixed at the highest point of the disc. Now the system is released, when the body comes to the lowest position, its angular speed will be 4√‌
x
3R
‌rad‌s−1 where x= ________. (g=10ms−2)
[26-Jul-2022-Shift-1]
Q.49 Correct
Q.49 In-correct
Q.49 Unattempt
The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be ______m.
Given, the length of the rod is 10√3m.
[26-Jul-2022-Shift-2]
The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be ______m.
Given, the length of the rod is 10√3m.
[26-Jul-2022-Shift-2]
Q.50 Correct
Q.50 In-correct
Q.50 Unattempt
A pulley of radius 1.5m is rotated about its axis by a force F=(12t−3t2)N applied tangentially (while t is measured in seconds). If moment of inertia of the pulley about its axis of rotation is 4.5‌kg‌m, the number of rotations made by the pulley before its direction of motion is reversed, will be ‌
K
π
. The value of K is ________.
[27-Jul-2022-Shift-1]
A pulley of radius 1.5m is rotated about its axis by a force F=(12t−3t2)N applied tangentially (while t is measured in seconds). If moment of inertia of the pulley about its axis of rotation is 4.5‌kg‌m, the number of rotations made by the pulley before its direction of motion is reversed, will be ‌
K
π
. The value of K is ________.
[27-Jul-2022-Shift-1]
Q.51 Correct
Q.51 In-correct
Q.51 Unattempt
As shown in the figure, a metallic rod of linear density 0.45‌kg‌m−1 is lying horizontally on a smooth inclined plane which makes an angle of 45∘ with the horizontal. The minimum current flowing in the rod required to keep it stationary, when 0.15T magnetic field is acting on it in the vertical upward direction, will be :
{. Use .g=10m∕s2}

[28-Jul-2022-Shift-1]
As shown in the figure, a metallic rod of linear density 0.45‌kg‌m−1 is lying horizontally on a smooth inclined plane which makes an angle of 45∘ with the horizontal. The minimum current flowing in the rod required to keep it stationary, when 0.15T magnetic field is acting on it in the vertical upward direction, will be :
{. Use .g=10m∕s2}

[28-Jul-2022-Shift-1]
Q.52 Correct
Q.52 In-correct
Q.52 Unattempt
The torque of a force 5
∧
i
+3
∧
j
−7
∧
k
 about the origin is τ. If the force acts on a particle whose position vector is 2i+2j+k, then the value of τ will be
[29-Jul-2022-Shift-2]
The torque of a force 5
∧
i
+3
∧
j
−7
∧
k
 about the origin is τ. If the force acts on a particle whose position vector is 2i+2j+k, then the value of τ will be
[29-Jul-2022-Shift-2]
Q.53 Correct
Q.53 In-correct
Q.53 Unattempt
Four identical solid spheres each of mass m and radius a are placed with their centres on the four corners of a square of side b. The moment of inertia of the system about one side of square, where the axis of rotation is parallel to the plane of the square is
[26 Feb 2021 Shift 1]
Four identical solid spheres each of mass m and radius a are placed with their centres on the four corners of a square of side b. The moment of inertia of the system about one side of square, where the axis of rotation is parallel to the plane of the square is
[26 Feb 2021 Shift 1]
Q.54 Correct
Q.54 In-correct
Q.54 Unattempt
A uniform thin bar of mass 6kg and length 2.4m is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is ..........×10−1kg−m2.
[24 Feb 2021 Shift 2]
A uniform thin bar of mass 6kg and length 2.4m is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is ..........×10−1kg−m2.
[24 Feb 2021 Shift 2]
Q.55 Correct
Q.55 In-correct
Q.55 Unattempt
Two masses A and B, each of mass M are fixed together by a massless spring. A force acts on the mass B as shown in figure. If the mass A starts moving away from mass B with acceleration a, then the acceleration of mass B will be

[26 Feb 2021 Shift 2]
Two masses A and B, each of mass M are fixed together by a massless spring. A force acts on the mass B as shown in figure. If the mass A starts moving away from mass B with acceleration a, then the acceleration of mass B will be

[26 Feb 2021 Shift 2]
Q.56 Correct
Q.56 In-correct
Q.56 Unattempt
A circular hole of radius (‌
a
2
) is cut out of a circular disc of radius a as shown in figure The centroid of the remaining circular portion with respect to point O will be

[24 Feb 2021 Shift 2]
A circular hole of radius (‌
a
2
) is cut out of a circular disc of radius a as shown in figure The centroid of the remaining circular portion with respect to point O will be

[24 Feb 2021 Shift 2]
Q.57 Correct
Q.57 In-correct
Q.57 Unattempt
A cord is wound round the circumference of wheel of radius r. The axis of the wheel is horizontal and the moment of inertia about it is I. A weight mg is attached to the cord at the end. The weight falls from rest. After falling through a distance h, the square of angular velocity of wheel will be
[26 Feb 2021 Shift 2]
A cord is wound round the circumference of wheel of radius r. The axis of the wheel is horizontal and the moment of inertia about it is I. A weight mg is attached to the cord at the end. The weight falls from rest. After falling through a distance h, the square of angular velocity of wheel will be
[26 Feb 2021 Shift 2]
Q.58 Correct
Q.58 In-correct
Q.58 Unattempt
A sphere of radius a and mass m rolls along a horizontal plane with constant speed v0. It encounters an inclined plane at angle θ and climbs upwards. Assuming that it rolls without slipping, how far up the sphere will travel?

[25 Feb 2021 Shift 2]
A sphere of radius a and mass m rolls along a horizontal plane with constant speed v0. It encounters an inclined plane at angle θ and climbs upwards. Assuming that it rolls without slipping, how far up the sphere will travel?

[25 Feb 2021 Shift 2]
Q.59 Correct
Q.59 In-correct
Q.59 Unattempt
Moment of inertia (M.I.) of four bodies, having same mass and radius, are reported as;
I1= M.I. of thin circular ring about its diameter,
I2= M.I. of circular disc about an axis perpendicular to the disc and going through the centre,
I3= M.I. of solid cylinder about its axis and I4= M.I. of solid sphere about its diameter. Then :
[24feb2021shift1]
Moment of inertia (M.I.) of four bodies, having same mass and radius, are reported as;
I1= M.I. of thin circular ring about its diameter,
I2= M.I. of circular disc about an axis perpendicular to the disc and going through the centre,
I3= M.I. of solid cylinder about its axis and I4= M.I. of solid sphere about its diameter. Then :
[24feb2021shift1]
Q.60 Correct
Q.60 In-correct
Q.60 Unattempt
A thin circular ring of mass M and radius r is rotating about its axis with an angular speed ๗. Two particles having mass m each are now attached at diametrically opposite points.
The angular speed of the ring will become
[18 Mar 2021 Shift 1]
A thin circular ring of mass M and radius r is rotating about its axis with an angular speed ๗. Two particles having mass m each are now attached at diametrically opposite points.
The angular speed of the ring will become
[18 Mar 2021 Shift 1]
Q.61 Correct
Q.61 In-correct
Q.61 Unattempt
The disc of mass M with uniform surface mass density σ is shown in the figure. The centre of mass of the quarter disc (the shaded area) is at the position ‌
x
3
‌
a
π
,‌
x
3
‌
a
π
, where x is ............ (Round off to the nearest integer) ( a is an area as shown in the figure)

[17 Mar 2021 Shift 2]
The disc of mass M with uniform surface mass density σ is shown in the figure. The centre of mass of the quarter disc (the shaded area) is at the position ‌
x
3
‌
a
π
,‌
x
3
‌
a
π
, where x is ............ (Round off to the nearest integer) ( a is an area as shown in the figure)

[17 Mar 2021 Shift 2]
Q.62 Correct
Q.62 In-correct
Q.62 Unattempt
A mass M hangs on a massless rod of length / which rotates at a constant angular frequency. The mass M moves with steady speed in a circular path of constant radius. Assume that the system is in steady circular motion with constant angular velocity ω. The angular momentum of M about point A is LA which lies in the positive z-direction and the angular momentum of M about B is LB. The correct statement for this system is

[17 Mar 2021 Shift 1]
A mass M hangs on a massless rod of length / which rotates at a constant angular frequency. The mass M moves with steady speed in a circular path of constant radius. Assume that the system is in steady circular motion with constant angular velocity ω. The angular momentum of M about point A is LA which lies in the positive z-direction and the angular momentum of M about B is LB. The correct statement for this system is

[17 Mar 2021 Shift 1]
Q.63 Correct
Q.63 In-correct
Q.63 Unattempt
A triangular plate is shown below. A force F=4
∧
i
−3
∧
j
 is applied at point P. The torque at point P with respect to point O and Q are

[17 Mar 2021 Shift 1]
A triangular plate is shown below. A force F=4
∧
i
−3
∧
j
 is applied at point P. The torque at point P with respect to point O and Q are

[17 Mar 2021 Shift 1]
Q.64 Correct
Q.64 In-correct
Q.64 Unattempt
A sphere of mass 2kg and radius 0.5m is rolling with an initial speed of 1ms−1 goes up an inclined plane which makes an angle of 30∘ with the horizontal plane, without slipping. How long will the sphere take to return to the starting point A ?

[17 Mar 2021 Shift 2]
A sphere of mass 2kg and radius 0.5m is rolling with an initial speed of 1ms−1 goes up an inclined plane which makes an angle of 30∘ with the horizontal plane, without slipping. How long will the sphere take to return to the starting point A ?

[17 Mar 2021 Shift 2]
Q.65 Correct
Q.65 In-correct
Q.65 Unattempt
The following bodies,
1. a ring
2. a disc
3. a solid cylinder
4. a solid sphere
of same mass m and radius R are allowed t roll down without slipping simultaneously from the top of the inclined plane. The boo which will reach first at the bottom of the inclined plane is .......... .
(Mark the body as per their respective numbering given in the question)

[17 Mar 2021 Shift 1]
The following bodies,
1. a ring
2. a disc
3. a solid cylinder
4. a solid sphere
of same mass m and radius R are allowed t roll down without slipping simultaneously from the top of the inclined plane. The boo which will reach first at the bottom of the inclined plane is .......... .
(Mark the body as per their respective numbering given in the question)

[17 Mar 2021 Shift 1]
Q.66 Correct
Q.66 In-correct
Q.66 Unattempt
The angular speed of truck wheel is increased from 900 rpm to 2460rpm in 26s. The number of revolutions by the truck engine during this time is .........
(Assuming the acceleration to be uniform).
[17 Mar 2021 Shift 1]
The angular speed of truck wheel is increased from 900 rpm to 2460rpm in 26s. The number of revolutions by the truck engine during this time is .........
(Assuming the acceleration to be uniform).
[17 Mar 2021 Shift 1]
Q.67 Correct
Q.67 In-correct
Q.67 Unattempt
A solid disc of radius a and mass m rolls down without slipping on an inclined plane making an angle θ with the horizontal. The acceleration of the disc will be ‌
2
b
g‌sin‌θ, where b is
(Round off to the nearest integer)
( g= acceleration due to gravity)
(theta= angle as shown in figure)

[16 Mar 2021 Shift 2]
A solid disc of radius a and mass m rolls down without slipping on an inclined plane making an angle θ with the horizontal. The acceleration of the disc will be ‌
2
b
g‌sin‌θ, where b is
(Round off to the nearest integer)
( g= acceleration due to gravity)
(theta= angle as shown in figure)

[16 Mar 2021 Shift 2]
Q.68 Correct
Q.68 In-correct
Q.68 Unattempt
Consider a 20kg uniform circular disc of radius 0.2m. It is pin supported at its centre and is at rest initially. The disc is acted upon by a constant force F=20N through a massless string wrapped around its periphery as shown in the figure.
Suppose the disc makes n number of revolutions to attain an angular speed of 50rads−1. The value of n to the nearest integer, is .......... .
(Given, in one complete revolution, the disc
[16 Mar 2021 Shift 1]
Consider a 20kg uniform circular disc of radius 0.2m. It is pin supported at its centre and is at rest initially. The disc is acted upon by a constant force F=20N through a massless string wrapped around its periphery as shown in the figure.

Suppose the disc makes n number of revolutions to attain an angular speed of 50rads−1. The value of n to the nearest integer, is .......... .
(Given, in one complete revolution, the disc
[16 Mar 2021 Shift 1]
Q.69 Correct
Q.69 In-correct
Q.69 Unattempt
A force F=4
∧
i
+3
∧
j
+4
∧
k
 is applied on an intersection point of x=2 plane and X-axis. The magnitude of torque of this force about a point (2,3,4) is .......
(Round off to the nearest integer)
[16 Mar 2021 Shift 2]
A force F=4
∧
i
+3
∧
j
+4
∧
k
 is applied on an intersection point of x=2 plane and X-axis. The magnitude of torque of this force about a point (2,3,4) is .......
(Round off to the nearest integer)
[16 Mar 2021 Shift 2]
Q.70 Correct
Q.70 In-correct
Q.70 Unattempt
Consider a uniform wire of mass M and length L. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the centre is
[18 Mar 2021 Shift 2]
Consider a uniform wire of mass M and length L. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the centre is
[18 Mar 2021 Shift 2]
Q.71 Correct
Q.71 In-correct
Q.71 Unattempt
Four equal masses, m each are placed at the corners of a square of length (I) as shown in the figure

[16 Mar 2021 Shift 1]
Four equal masses, m each are placed at the corners of a square of length (I) as shown in the figure

[16 Mar 2021 Shift 1]
Q.72 Correct
Q.72 In-correct
Q.72 Unattempt
A solid disc of radius 20cm and mass 10kg is rotating with an angular velocity of 600 rpm, about an axis normal to its circular plane and passing through its centre of mass. The retarding torque required to bring the disc at rest in 10s is _____ π×10−1Nm.
[25 Jul 2021 Shift 2]
A solid disc of radius 20cm and mass 10kg is rotating with an angular velocity of 600 rpm, about an axis normal to its circular plane and passing through its centre of mass. The retarding torque required to bring the disc at rest in 10s is _____ π×10−1Nm.
[25 Jul 2021 Shift 2]
Q.73 Correct
Q.73 In-correct
Q.73 Unattempt
A body of mass 2 kg moving with a speed of 4 m/s. makes an elastic collision with another body at rest and continues to move in the original direction but with one fourth of its initial speed.
The speed of the two body centre of mass is
x
10
m / s . Then the value of x is_______.
[25 Jul 2021 Shift 1]
A body of mass 2 kg moving with a speed of 4 m/s. makes an elastic collision with another body at rest and continues to move in the original direction but with one fourth of its initial speed.
The speed of the two body centre of mass is
x
10
m / s . Then the value of x is_______.
[25 Jul 2021 Shift 1]
Q.74 Correct
Q.74 In-correct
Q.74 Unattempt
A particle of mass 'm' is moving in time 't' on a trajectory given by
→
r
=10αt2
^
i
+5β(t−5)
^
j
Where α and β are dimensional constants.
The angular momentum of the particle becomes the same as it was for t = 0 at time t = ______seconds.
[25 Jul 2021 Shift 1]
A particle of mass 'm' is moving in time 't' on a trajectory given by
→
r
=10αt2
^
i
+5β(t−5)
^
j
Where α and β are dimensional constants.
The angular momentum of the particle becomes the same as it was for t = 0 at time t = ______seconds.
[25 Jul 2021 Shift 1]
Q.75 Correct
Q.75 In-correct
Q.75 Unattempt
The position of the centre of mass of a uniform semi-circular wire of radius 'R' placed in x−y plane with its centre at the origin and the line joining its ends as x-axis is given by (0,
xR
π
).
Then, the value of |x| is __________.
[22 Jul 2021 Shift 2]
The position of the centre of mass of a uniform semi-circular wire of radius 'R' placed in x−y plane with its centre at the origin and the line joining its ends as x-axis is given by (0,
xR
π
).
Then, the value of |x| is __________.
[22 Jul 2021 Shift 2]
Q.76 Correct
Q.76 In-correct
Q.76 Unattempt
A rod of mass M and length L is lying on a horizontal frictionless surface. A particle of mass 'm' travelling along the surface hits at one end of the rod with a velocity 'u' in a direction perpendicular to the rod. The collision is completely elastic. After collision, particle comes to rest. The ratio of masses (
m
M
) is
1
x
. The value of ' x ' will be ______.
[20 Jul 2021 Shift 1]
A rod of mass M and length L is lying on a horizontal frictionless surface. A particle of mass 'm' travelling along the surface hits at one end of the rod with a velocity 'u' in a direction perpendicular to the rod. The collision is completely elastic. After collision, particle comes to rest. The ratio of masses (
m
M
) is
1
x
. The value of ' x ' will be ______.
[20 Jul 2021 Shift 1]
Q.77 Correct
Q.77 In-correct
Q.77 Unattempt

Choose the correct answer from the options given below :
[27 Jul 2021 Shift 1]

Choose the correct answer from the options given below :
[27 Jul 2021 Shift 1]
Q.78 Correct
Q.78 In-correct
Q.78 Unattempt
The figure shows two solid discs with radius R and r respectively. If mass per unit area is same for both, what is the ratio of MI of bigger disc around axis AB (Which is ⊥ to the plane of the disc and passing through its centre) of MI of smaller disc around one of its diameters lying on its plane?
Given 'M' is the mass of the larger disc. (MI stands for moment of inertia)

[27 Jul 2021 Shift 1]
The figure shows two solid discs with radius R and r respectively. If mass per unit area is same for both, what is the ratio of MI of bigger disc around axis AB (Which is ⊥ to the plane of the disc and passing through its centre) of MI of smaller disc around one of its diameters lying on its plane?
Given 'M' is the mass of the larger disc. (MI stands for moment of inertia)

[27 Jul 2021 Shift 1]
Q.79 Correct
Q.79 In-correct
Q.79 Unattempt
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Moment of inertia of a circular disc of mass ' M ' and radius 'R' about X,Y axes (passing through its plane) and Z-axis which is perpendicular to its plane were found to be Ix,Iy and Iz respectively. The respective radii of gyration about all the three axes will be the same.
Reason R : A rigid body making rotational motion has fixed mass and shape. In the light of the above statements, choose the most appropriate answer from the options given below:
[25 Jul 2021 Shift 1]
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Moment of inertia of a circular disc of mass ' M ' and radius 'R' about X,Y axes (passing through its plane) and Z-axis which is perpendicular to its plane were found to be Ix,Iy and Iz respectively. The respective radii of gyration about all the three axes will be the same.
Reason R : A rigid body making rotational motion has fixed mass and shape. In the light of the above statements, choose the most appropriate answer from the options given below:
[25 Jul 2021 Shift 1]
Q.80 Correct
Q.80 In-correct
Q.80 Unattempt
In the given figure, two wheels P and Q are connected by a belt B. The radius of P is three times as that of Q. In case of same rotational kinetic energy, the ratio of rotational inertias (
I1
I2
)will be x:1. The value of x will be ______.

[27 Jul 2021 Shift 2]
In the given figure, two wheels P and Q are connected by a belt B. The radius of P is three times as that of Q. In case of same rotational kinetic energy, the ratio of rotational inertias (
I1
I2
)will be x:1. The value of x will be ______.

[27 Jul 2021 Shift 2]
Q.81 Correct
Q.81 In-correct
Q.81 Unattempt
The centre of a wheel rolling on a plane surface moves with a speed v0. A particle on the rim of the wheel at the same level as the centre will be moving at a speed √xv0. Then the value of x is _______.
[22 Jul 2021 Shift 2]
The centre of a wheel rolling on a plane surface moves with a speed v0. A particle on the rim of the wheel at the same level as the centre will be moving at a speed √xv0. Then the value of x is _______.
[22 Jul 2021 Shift 2]
Q.82 Correct
Q.82 In-correct
Q.82 Unattempt
Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without slipping. Assume that they start rolling from rest and having identical diameter.
The correct statement for this situation is:-
[22 Jul 2021 Shift 2]
Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without slipping. Assume that they start rolling from rest and having identical diameter.
The correct statement for this situation is:-
[22 Jul 2021 Shift 2]
Q.83 Correct
Q.83 In-correct
Q.83 Unattempt
A body rolls down an inclined plane without slipping. The kinetic energy of rotation is 50% of its translational kinetic energy. The body is :
[20 Jul 2021 Shift 2]
A body rolls down an inclined plane without slipping. The kinetic energy of rotation is 50% of its translational kinetic energy. The body is :
[20 Jul 2021 Shift 2]
Q.84 Correct
Q.84 In-correct
Q.84 Unattempt
A circular disc reaches from top to bottom of an inclined plane of length ' L′. When it slips down the plane, it takes time ' t1′. When it rolls down the plane, it takes time t2. The value of
t2
t1
 is √
3
x
. The value of x will be ______.
[20 Jul 2021 Shift 1]
A circular disc reaches from top to bottom of an inclined plane of length ' L′. When it slips down the plane, it takes time ' t1′. When it rolls down the plane, it takes time t2. The value of
t2
t1
 is √
3
x
. The value of x will be ______.
[20 Jul 2021 Shift 1]
Q.85 Correct
Q.85 In-correct
Q.85 Unattempt
Two bodies, a ring and a solid cylinder of same material are rolling down without slipping an inclined plane. The radii of the bodies are same. The ratio of velocity of the centre of mass at the bottom of the inclined plane of the ring to that of the cylinder is
√x
2
. Then, the value of x is _____.
[20 Jul 2021 Shift 2]
Two bodies, a ring and a solid cylinder of same material are rolling down without slipping an inclined plane. The radii of the bodies are same. The ratio of velocity of the centre of mass at the bottom of the inclined plane of the ring to that of the cylinder is
√x
2
. Then, the value of x is _____.
[20 Jul 2021 Shift 2]
Q.86 Correct
Q.86 In-correct
Q.86 Unattempt
A body rotating with an angular speed of 600 rpm is uniformly accelerated to 1800 rpm in 10 sec. The number of rotations made in the process is___.
[20 Jul 2021 Shift 2]
A body rotating with an angular speed of 600 rpm is uniformly accelerated to 1800 rpm in 10 sec. The number of rotations made in the process is___.
[20 Jul 2021 Shift 2]
Q.87 Correct
Q.87 In-correct
Q.87 Unattempt
Angular momentum of a single particle moving with constant speed along circular path
[31 Aug 2021 Shift 1]
Angular momentum of a single particle moving with constant speed along circular path
[31 Aug 2021 Shift 1]
Q.88 Correct
Q.88 In-correct
Q.88 Unattempt
A system consists of two identical spheres each of mass 1.5‌kg and radius 50‌cm at the end of light rod. The distance between the centres of the two spheres is 5m. What will be the moment of inertia of the system about an axis perpendicular to the rod passing through its mid-point?
[31 Aug 2021 Shift 2]
A system consists of two identical spheres each of mass 1.5‌kg and radius 50‌cm at the end of light rod. The distance between the centres of the two spheres is 5m. What will be the moment of inertia of the system about an axis perpendicular to the rod passing through its mid-point?
[31 Aug 2021 Shift 2]
Q.89 Correct
Q.89 In-correct
Q.89 Unattempt
Moment of inertia of a square plate of side / about the axis passing through one of the corner and perpendicular to the plane of square plate is given by
[27 Aug 2021 Shift 1]
Moment of inertia of a square plate of side / about the axis passing through one of the corner and perpendicular to the plane of square plate is given by
[27 Aug 2021 Shift 1]
Q.90 Correct
Q.90 In-correct
Q.90 Unattempt
The solid cylinder of length 80‌cm and mass M has a radius of 20‌cm. Calculate the density of the material used, if the moment of inertia of the cylinder about an axis CD parallel to AB as shown in figure is 2.7‌kg‌m2.

[26 Aug 2021 Shift 2]
The solid cylinder of length 80‌cm and mass M has a radius of 20‌cm. Calculate the density of the material used, if the moment of inertia of the cylinder about an axis CD parallel to AB as shown in figure is 2.7‌kg‌m2.

[26 Aug 2021 Shift 2]
Q.91 Correct
Q.91 In-correct
Q.91 Unattempt
Consider a badminton racket with length scales as shown in the figure.
If the mass of the linear and circular portions of the badminton racket are same (M) and the mass of the threads are negligible, the moment of inertia of the racket about an axis perpendicular to the handle and in the plane of the ring at,
r
2
 distance from the end A of the
handle will be ........ Mr2.
[26 Aug 2021 Shift 1]
Consider a badminton racket with length scales as shown in the figure.

If the mass of the linear and circular portions of the badminton racket are same (M) and the mass of the threads are negligible, the moment of inertia of the racket about an axis perpendicular to the handle and in the plane of the ring at,
r
2
 distance from the end A of the
handle will be ........ Mr2.
[26 Aug 2021 Shift 1]
Q.92 Correct
Q.92 In-correct
Q.92 Unattempt
Two discs have moments of inertia I1 and I2 about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, ω1 and ω2 respectively and are brought into contact face to face with their axes of rotation co-axial. The loss in kinetic energy of the system in the process is given by
[27 Aug 2021 Shift 2]
Two discs have moments of inertia I1 and I2 about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, ω1 and ω2 respectively and are brought into contact face to face with their axes of rotation co-axial. The loss in kinetic energy of the system in the process is given by
[27 Aug 2021 Shift 2]
Q.93 Correct
Q.93 In-correct
Q.93 Unattempt
A 2‌kg steel rod of length 0.6m is clamped on a table vertically at its lower end and is free to rotate in vertical plane. The upper end is pushed so that the rod falls under gravity. Ignoring the friction due to clamping at its lower end, the speed of the free end of rod when it passes through its lowest position is ........... ms−1.
(Take, g=10ms−2 )
[1 Sep 2021 Shift 2]
A 2‌kg steel rod of length 0.6m is clamped on a table vertically at its lower end and is free to rotate in vertical plane. The upper end is pushed so that the rod falls under gravity. Ignoring the friction due to clamping at its lower end, the speed of the free end of rod when it passes through its lowest position is ........... ms−1.
(Take, g=10ms−2 )
[1 Sep 2021 Shift 2]
Q.94 Correct
Q.94 In-correct
Q.94 Unattempt
A rod of length L has non-uniform linear mass density given by ρ(x)=a+b(
x
L
)2, where a and b are constants and 0≤x≤L. The value of x for the centre of mass of the rod is at:
[9 Jan. 2020 II]
A rod of length L has non-uniform linear mass density given by ρ(x)=a+b(
x
L
)2, where a and b are constants and 0≤x≤L. The value of x for the centre of mass of the rod is at:
[9 Jan. 2020 II]
Q.95 Correct
Q.95 In-correct
Q.95 Unattempt
The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass 4kg. (The coordinates of the same are shown in figure) are:

[8 Jan. 2020 I]
The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass 4kg. (The coordinates of the same are shown in figure) are:

[8 Jan. 2020 I]
Q.96 Correct
Q.96 In-correct
Q.96 Unattempt
As shown in fig. when a spherical cavity (centred at O ) of radius 1 is cut out of a uniform sphere of radius R (centred at C ), the centre of mass of remaining (shaded) part of sphere is at G, i.e on the surface of the cavity. R can be determined by the equation:

[8 Jan. 2020 II]
As shown in fig. when a spherical cavity (centred at O ) of radius 1 is cut out of a uniform sphere of radius R (centred at C ), the centre of mass of remaining (shaded) part of sphere is at G, i.e on the surface of the cavity. R can be determined by the equation:

[8 Jan. 2020 II]
Q.97 Correct
Q.97 In-correct
Q.97 Unattempt
Three point particles of masses 1.0kg,1.5kg and 2.5kg are placed at three corners of a right angle triangle of sides 4.0cm,3.0cm and 5.0cm as shown in the figure. The center of mass of the system is at a point:
[7 Jan. 2020 I]
Three point particles of masses 1.0kg,1.5kg and 2.5kg are placed at three corners of a right angle triangle of sides 4.0cm,3.0cm and 5.0cm as shown in the figure. The center of mass of the system is at a point:
[7 Jan. 2020 I]
Q.98 Correct
Q.98 In-correct
Q.98 Unattempt
A spring mass system (mass m, spring constant k and natural length l ) rests in equilibrium on a horizontal disc. The free end of the spring is fixed at the centre of the disc. If the disc together with spring mass system, rotates about it's axis with an angular velocity ω,(k>>mω2) the relative change in the length of the spring is best given by the option:
[9 Jan. 2020 II]
A spring mass system (mass m, spring constant k and natural length l ) rests in equilibrium on a horizontal disc. The free end of the spring is fixed at the centre of the disc. If the disc together with spring mass system, rotates about it's axis with an angular velocity ω,(k>>mω2) the relative change in the length of the spring is best given by the option:
[9 Jan. 2020 II]
Q.99 Correct
Q.99 In-correct
Q.99 Unattempt
A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length l. The other end is fixed. The system is given an angular speed omega about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is:
[8 Jan. 2020 I]
A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length l. The other end is fixed. The system is given an angular speed omega about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is:
[8 Jan. 2020 I]
Q.100 Correct
Q.100 In-correct
Q.100 Unattempt
Consider a uniform rod of mass M=4m and length l pivoted about its centre. A mass m moving with velocity v makingangle θ=
π
4
 to the rod's long axis collides with one end of the rod and sticks to it. The angular speed of the rod-mass system just after the collision is:
[8 Jan. 2020 I]
Consider a uniform rod of mass M=4m and length l pivoted about its centre. A mass m moving with velocity v makingangle θ=
π
4
 to the rod's long axis collides with one end of the rod and sticks to it. The angular speed of the rod-mass system just after the collision is:
[8 Jan. 2020 I]
Q.101 Correct
Q.101 In-correct
Q.101 Unattempt
Three solid spheres each of mass m and diameter d are stuck together such that the lines connecting the centres form an equilateral triangle of side of length d. The ratio
I0
IA
 of moment of inertia I0 of the system about an axis passing the centroid and about center of any of the spheres IA and perpendicular to the plane of the triangle is:

[9 Jan. 2020 I]
Three solid spheres each of mass m and diameter d are stuck together such that the lines connecting the centres form an equilateral triangle of side of length d. The ratio
I0
IA
 of moment of inertia I0 of the system about an axis passing the centroid and about center of any of the spheres IA and perpendicular to the plane of the triangle is:

[9 Jan. 2020 I]
Q.102 Correct
Q.102 In-correct
Q.102 Unattempt
One end of a straight uniform 1m long bar is pivoted on horizontal table. It is released from rest when it makes an angle 30° from the horizontal (see figure). Its angular speed when it hits the table is given as √ns−1, where n is an integer. The value of n is ________.

[9 Jan. 2020 I]
One end of a straight uniform 1m long bar is pivoted on horizontal table. It is released from rest when it makes an angle 30° from the horizontal (see figure). Its angular speed when it hits the table is given as √ns−1, where n is an integer. The value of n is ________.

[9 Jan. 2020 I]
Q.103 Correct
Q.103 In-correct
Q.103 Unattempt
A uniformly thick wheel with moment of inertia I and radius R is free to rotate about its centre of mass (see fig). A massless string is wrapped over its rim and two blocks of masses m1 and m2(m1>m2) are attached to the ends of the string. The system is released from rest. The angular speed of the wheel when m1 descents by a distance h is:

[9 Jan. 2020 II]
A uniformly thick wheel with moment of inertia I and radius R is free to rotate about its centre of mass (see fig). A massless string is wrapped over its rim and two blocks of masses m1 and m2(m1>m2) are attached to the ends of the string. The system is released from rest. The angular speed of the wheel when m1 descents by a distance h is:

[9 Jan. 2020 II]
Q.104 Correct
Q.104 In-correct
Q.104 Unattempt
As shown in the figure, a bob of mass m is tied by a massless string whose other end portion is wound on a fly wheel (disc) of radius r and mass m. When released from rest the bob starts falling vertically. When it has covered a distance of h, the angular speed of the wheel will be:

[7 Jan. 2020 I]
As shown in the figure, a bob of mass m is tied by a massless string whose other end portion is wound on a fly wheel (disc) of radius r and mass m. When released from rest the bob starts falling vertically. When it has covered a distance of h, the angular speed of the wheel will be:

[7 Jan. 2020 I]
Q.105 Correct
Q.105 In-correct
Q.105 Unattempt
The radius of gyration of a uniform rod of length l, about an axis passing through a point
l
4
 away from the centre of the rod, and perpendicular to it, is:
[7 Jan. 2020 I]
The radius of gyration of a uniform rod of length l, about an axis passing through a point
l
4
 away from the centre of the rod, and perpendicular to it, is:
[7 Jan. 2020 I]
Q.106 Correct
Q.106 In-correct
Q.106 Unattempt
Mass per unit area of a circular disc of radius a depends on the distance r from its centre as σ(r)=A+Br. The moment of inertia of the disc about the axis, perpendicular to the plane and passing through its centre is:
[7 Jan. 2020 II]
Mass per unit area of a circular disc of radius a depends on the distance r from its centre as σ(r)=A+Br. The moment of inertia of the disc about the axis, perpendicular to the plane and passing through its centre is:
[7 Jan. 2020 II]
Q.107 Correct
Q.107 In-correct
Q.107 Unattempt
A uniform sphere of mass 500g rolls without slipping on a plane horizontal surface with its centre moving at a speed of 5.00cm∕s. Its kinetic energy is:
[8 Jan. 2020 II]
A uniform sphere of mass 500g rolls without slipping on a plane horizontal surface with its centre moving at a speed of 5.00cm∕s. Its kinetic energy is:
[8 Jan. 2020 II]
Q.108 Correct
Q.108 In-correct
Q.108 Unattempt
Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible force F at a point b above its centre of mass (see figure). If the coefficient of friction is µ=0.4, the maximum possible value of 100×
b
a
 for box not to topple before moving is ______.
[NA 7 Jan. 2020 II]

Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible force F at a point b above its centre of mass (see figure). If the coefficient of friction is µ=0.4, the maximum possible value of 100×
b
a
 for box not to topple before moving is ______.
[NA 7 Jan. 2020 II]
Q.109 Correct
Q.109 In-correct
Q.109 Unattempt
The centre of mass of a solid hemisphere of radius 8cm is xcm from the centre of the flat surface. Then value of x is_______.
[NA Sep. 06, 2020 (II)]
The centre of mass of a solid hemisphere of radius 8cm is xcm from the centre of the flat surface. Then value of x is_______.
[NA Sep. 06, 2020 (II)]
Q.110 Correct
Q.110 In-correct
Q.110 Unattempt
A square shaped hole of side l=
a
2
 is carved out at a distance d=
a
2
 from the centre ' O ' of a uniform circular disk of radius a. If the distance of the centre of mass of the remaining portion from O is −
a
X
, value of X( to the nearest integer) is _______.

[NA Sep. 02, 2020 (II)]
A square shaped hole of side l=
a
2
 is carved out at a distance d=
a
2
 from the centre ' O ' of a uniform circular disk of radius a. If the distance of the centre of mass of the remaining portion from O is −
a
X
, value of X( to the nearest integer) is _______.

[NA Sep. 02, 2020 (II)]
Q.111 Correct
Q.111 In-correct
Q.111 Unattempt
A bead of mass m stays at point P(a,b) on a wire bent in the shape of a parabola y=4Cx2 and rotating with angular speed ω (see figure). The value of ω is (neglect friction):

[Sep. 02, 2020 (I)]
A bead of mass m stays at point P(a,b) on a wire bent in the shape of a parabola y=4Cx2 and rotating with angular speed ω (see figure). The value of ω is (neglect friction):

[Sep. 02, 2020 (I)]
Q.112 Correct
Q.112 In-correct
Q.112 Unattempt
A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is 5cm and the angular speed of rotation is ω‌rad‌s−1. The difference in the height, h (in cm ) of liquid at the centre of vessel and at the side will be :

[Sep. 02, 2020 (I)]
A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is 5cm and the angular speed of rotation is ω‌rad‌s−1. The difference in the height, h (in cm ) of liquid at the centre of vessel and at the side will be :

[Sep. 02, 2020 (I)]
Q.113 Correct
Q.113 In-correct
Q.113 Unattempt
Four point masses, each of mass m, are fixed at the corners of a square of side l. The square is rotating with angular frequency omega, about an axis passing through one of the corners of the square and parallel to its diagonal, as shown in the figure. The angular momentum of the square about this axis is :

[Sep. 06, 2020 (I)]
Four point masses, each of mass m, are fixed at the corners of a square of side l. The square is rotating with angular frequency omega, about an axis passing through one of the corners of the square and parallel to its diagonal, as shown in the figure. The angular momentum of the square about this axis is :

[Sep. 06, 2020 (I)]
Q.114 Correct
Q.114 In-correct
Q.114 Unattempt
A thin rod of mass 0.9kg and length 1m is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of move 0.1kg moving in a straight line with velocity 80m∕s hits the rod at its bottom most point and sticks to it (see figure). The angular speed (in rad/s) of the rod immediately after the collision will be __________.
[NA Sep. 05, 2020 (II)]
A thin rod of mass 0.9kg and length 1m is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of move 0.1kg moving in a straight line with velocity 80m∕s hits the rod at its bottom most point and sticks to it (see figure). The angular speed (in rad/s) of the rod immediately after the collision will be __________.
[NA Sep. 05, 2020 (II)]
Q.115 Correct
Q.115 In-correct
Q.115 Unattempt
A person of 80kg mass is standing on the rim of a circular platform of mass 200kg rotating about its axis at 5 revolutions per minute (rpm). The person now starts moving towards the centre of the platform. What will be the rotational speed (in rpm) of the platform when the person reaches its centre _______.
[NA Sep. 03, 2020 (I)]
A person of 80kg mass is standing on the rim of a circular platform of mass 200kg rotating about its axis at 5 revolutions per minute (rpm). The person now starts moving towards the centre of the platform. What will be the rotational speed (in rpm) of the platform when the person reaches its centre _______.
[NA Sep. 03, 2020 (I)]
Q.116 Correct
Q.116 In-correct
Q.116 Unattempt
A block of mass m=1kg slides with velocity v=6m∕s on a frictionless horizontal surface and collides with a uniform vertical rod and sticks to it as shown. The rod is pivoted about O and swings as a result of the collision making angle θ before momentarily coming to rest. If the rod has mass M=2kg, and length l=1m, the value of θ is approximately: (take g=10m∕s2)

[Sep. 03, 2020 (I)]
A block of mass m=1kg slides with velocity v=6m∕s on a frictionless horizontal surface and collides with a uniform vertical rod and sticks to it as shown. The rod is pivoted about O and swings as a result of the collision making angle θ before momentarily coming to rest. If the rod has mass M=2kg, and length l=1m, the value of θ is approximately: (take g=10m∕s2)

[Sep. 03, 2020 (I)]
Q.117 Correct
Q.117 In-correct
Q.117 Unattempt
A uniform rod of length ' l ' is pivoted at one of its ends on a vertical shaft of negligible radius. When the shaft rotates at angular speed ω the rod makes an angle θ with it (see figure). To find θ equate the rate of change of angular momentum (direction going into the paper)
ml2
12
ω2‌sin‌θ‌cos‌θ about the centre of mass (CM) to the torque provided by the horizontal and vertical forces FH and FV about the CM. The value of θ is then such that :
[Sep. 03, 2020 (II)]

A uniform rod of length ' l ' is pivoted at one of its ends on a vertical shaft of negligible radius. When the shaft rotates at angular speed ω the rod makes an angle θ with it (see figure). To find θ equate the rate of change of angular momentum (direction going into the paper)
ml2
12
ω2‌sin‌θ‌cos‌θ about the centre of mass (CM) to the torque provided by the horizontal and vertical forces FH and FV about the CM. The value of θ is then such that :
[Sep. 03, 2020 (II)]
Q.118 Correct
Q.118 In-correct
Q.118 Unattempt
Shown in the figure is rigid and uniform one meter long rod‌A‌B held in horizontal position by two strings tied to its ends and attached to the ceiling. The rod is of mass 'm' and has another weight of mass 2m hung at a distance of 75cm from A. The tension in the string at A is:
[Sep. 02, 2020 (I)]

Shown in the figure is rigid and uniform one meter long rod‌A‌B held in horizontal position by two strings tied to its ends and attached to the ceiling. The rod is of mass 'm' and has another weight of mass 2m hung at a distance of 75cm from A. The tension in the string at A is:
[Sep. 02, 2020 (I)]
Q.119 Correct
Q.119 In-correct
Q.119 Unattempt
A uniform cylinder of mass M and radius R is to be pulled over a step of height a(a<R) by applying a force F at its centre ' O ' perpendicular to the plane through the axes of the cylinder on the edge of the step (see figure). The minimum value of F required is :

[Sep. 02, 2020 (I)]
A uniform cylinder of mass M and radius R is to be pulled over a step of height a(a<R) by applying a force F at its centre ' O ' perpendicular to the plane through the axes of the cylinder on the edge of the step (see figure). The minimum value of F required is :

[Sep. 02, 2020 (I)]
Q.120 Correct
Q.120 In-correct
Q.120 Unattempt
Shown in the figure is a hollow ice cream cone (it is open at the top). If its mass is M, radius of its top, R and height, H, then its moment of inertia about its axis is :

[Sep. 06, 2020 (I)]
Shown in the figure is a hollow icecream cone (it is open at the top). If its mass is M, radius of its top, R and height, H, then its moment of inertia about its axis is :

[Sep. 06, 2020 (I)]
Q.121 Correct
Q.121 In-correct
Q.121 Unattempt
The linear mass density of a thin rod AB of length L varies from A to B as λ(x)=λ0(1+
x
L
), where x is the distance from A. If M is the mass of the rod then its moment of inertia about an axis passing through A and perpendicular to the rod is:
[Sep. 06, 2020 (II)]
The linear mass density of a thin rod AB of length L varies from A to B as λ(x)=λ0(1+
x
L
), where x is the distance from A. If M is the mass of the rod then its moment of inertia about an axis passing through A and perpendicular to the rod is:
[Sep. 06, 2020 (II)]
Q.122 Correct
Q.122 In-correct
Q.122 Unattempt
A wheel is rotating freely with an angular speed w on a shaft. The moment of inertia of the wheel is I and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia 3I initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is :
[Sep. 05, 2020 (I)]
A wheel is rotating freely with an angular speed w on a shaft. The moment of inertia of the wheel is I and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia 3I initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is :
[Sep. 05, 2020 (I)]
Q.123 Correct
Q.123 In-correct
Q.123 Unattempt
ABC is a plane lamina of the shape of an equilateral triangle. D, E are mid points of AB, AC and G is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through G and perpendicular to the plane ABC is I0 . If part ADE is removed, the moment of inertia of the remaining part about the same axis is
NI0
16
 where N is an integer. Value of N is _______.

[NA Sep. 04, 2020 (I)]
ABC is a plane lamina of the shape of an equilateral triangle. D, E are mid points of AB, AC and G is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through G and perpendicular to the plane ABC is I0 . If part ADE is removed, the moment of inertia of the remaining part about the same axis is
NI0
16
 where N is an integer. Value of N is _______.

[NA Sep. 04, 2020 (I)]
Q.124 Correct
Q.124 In-correct
Q.124 Unattempt
A circular disc of mass M and radius R is rotating about its axis with angular speed ω1 . If another stationary dischaving radius
R
2
 and same mass M is dropped co-axially on to the rotating disc. Gradually both discs attain constant angular speed ω1 . The energy lost in the process is p% of the initial energy. Value of p is ___________.
[NA Sep. 04, 2020 (I)]
A circular disc of mass M and radius R is rotating about its axis with angular speed ω1 . If another stationary dischaving radius
R
2
 and same mass M is dropped co-axially on to the rotating disc. Gradually both discs attain constant angular speed ω1 . The energy lost in the process is p% of the initial energy. Value of p is ___________.
[NA Sep. 04, 2020 (I)]
Q.125 Correct
Q.125 In-correct
Q.125 Unattempt
Consider two uniform discs of the same thickness and different radii R1=R and R2=αR made of the same material. If the ratio of their moments of inertia I1 and I2, respectively, about their axes is I1:I2=1:16 then the value of α is :
[Sep. 04, 2020 (II)]
Consider two uniform discs of the same thickness and different radii R1=R and R2=αR made of the same material. If the ratio of their moments of inertia I1 and I2, respectively, about their axes is I1:I2=1:16 then the value of α is :
[Sep. 04, 2020 (II)]
Q.126 Correct
Q.126 In-correct
Q.126 Unattempt
For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through O (the centre of mass) and O' (corner point) is :
[Sep. 04, 2020 (II)]
For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through O (the centre of mass) and O' (corner point) is :
[Sep. 04, 2020 (II)]
Q.127 Correct
Q.127 In-correct
Q.127 Unattempt
Moment of inertia of a cylinder of mass M, length L and radius R about an axis passing through its centre and perpendicular to the axis of the cylinder isI=M(
R2
4
+
L2
12
). If such a cylinder is to be made for a given mass of a material, the ratio L∕R for it to have minimum possible I is:
[Sep. 03, 2020 (I)]
Moment of inertia of a cylinder of mass M, length L and radius R about an axis passing through its centre and perpendicular to the axis of the cylinder isI=M(
R2
4
+
L2
12
). If such a cylinder is to be made for a given mass of a material, the ratio L∕R for it to have minimum possible I is:
[Sep. 03, 2020 (I)]
Q.128 Correct
Q.128 In-correct
Q.128 Unattempt
An massless equilateral triangle EFG of side ' a ' (As shown in figure) has three particles of mass m situated at its vertices. The moment of inertia of the system about the line EX perpendicular to EG in the plane of EFG is
N
20
ma2 where N is an integer. The value of N is _______.

[Sep. 03, 2020 (II)]
An massless equilateral triangle EFG of side ' a ' (As shown in figure) has three particles of mass m situated at its vertices. The moment of inertia of the system about the line EX perpendicular to EG in the plane of EFG is
N
20
ma2 where N is an integer. The value of N is _______.

[Sep. 03, 2020 (II)]
Q.129 Correct
Q.129 In-correct
Q.129 Unattempt
Two uniform circular discs are rotating independently in the same direction around their common axis passing through their centres. The moment of inertia and angular velocity of the first disc are 0.1kg−m2 and 10rads−1 respectively while those for the second one are 0.2kg−m2 and 5rads−1 respectively. At some instant they get stuck together and start rotating as a single system about their common axis with some angular speed. The kinetic energy of the combined system is:
[Sep. 02,2020 (II)]
Two uniform circular discs are rotating independently in the same direction around their common axis passing through their centres. The moment of inertia and angular velocity of the first disc are 0.1kg−m2 and 10rads−1 respectively while those for the second one are 0.2kg−m2 and 5rads−1 respectively. At some instant they get stuck together and start rotating as a single system about their common axis with some angular speed. The kinetic energy of the combined system is:
[Sep. 02,2020 (II)]
Q.130 Correct
Q.130 In-correct
Q.130 Unattempt
A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5cm and its rotational speed is 2 rotations per second, then the difference in the heights between the centre and the sides, in cm, will be :
[12 Jan. 2019 II]
A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5cm and its rotational speed is 2 rotations per second, then the difference in the heights between the centre and the sides, in cm, will be :
[12 Jan. 2019 II]
Q.131 Correct
Q.131 In-correct
Q.131 Unattempt
A particle of mass 20g is released with an initial velocity 5m∕s along the curve from the point A, as shown in the figure. The point A is at height h from point B. The particle slides along the frictionless surface. When the particle reaches point B, its angular momentum about O will be :(Take g=10m∕s2)

[12 Jan. 2019 II]
A particle of mass 20g is released with an initial velocity 5m∕s along the curve from the point A, as shown in the figure. The point A is at height h from point B. The particle slides along the frictionless surface. When the particle reaches point B, its angular momentum about O will be :(Take g=10m∕s2)

[12 Jan. 2019 II]
Q.132 Correct
Q.132 In-correct
Q.132 Unattempt
The position vector of the centre of mass‌rcm of an asymmetric uniform bar of negligible area of cross section as shown in figure is:

[12 Jan. 2019 I]
The position vector of the centre of mass‌rcm of an asymmetric uniform bar of negligible area of cross section as shown in figure is:

[12 Jan. 2019 I]
Q.133 Correct
Q.133 In-correct
Q.133 Unattempt
A slab is subjected to two forces
→
F
1 and
→
F
2 of same magnitude F as shown in the figure. Force
→
F
2 is in XY-plane while force F1 acts along z -axis at the point(2
→
i
+3
→
j
). The moment of these forces about point O will be :

[11 Jan. 2019 I]
A slab is subjected to two forces
→
F
1 and
→
F
2 of same magnitude F as shown in the figure. Force
→
F
2 is in XY-plane while force F1 acts along z -axis at the point(2
→
i
+3
→
j
). The moment of these forces about point O will be :

[11 Jan. 2019 I]
Q.134 Correct
Q.134 In-correct
Q.134 Unattempt
The magnitude of torque on a particle of mass 1kg is 2.5 Nm about the origin. If the force acting on it is 1N, and the distance of the particle from the origin is 5m, the angle between the force and the position vector is (in radians):
[11 Jan. 2019 II]
The magnitude of torque on a particle of mass 1kg is 2.5 Nm about the origin. If the force acting on it is 1N, and the distance of the particle from the origin is 5m, the angle between the force and the position vector is (in radians):
[11 Jan. 2019 II]
Q.135 Correct
Q.135 In-correct
Q.135 Unattempt
To mop-clean a floor, a cleaning machine presses a circular mop of radius R vertically down with a total force F and rotates it with a constant angular speed about its axis. If the force F is distributed uniformly over the mop and if coefficient of friction between the mop and the floor is µ, the torque, applied by the machine on the mop is:
[10 Jan. 2019 I]
To mop-clean a floor, a cleaning machine presses a circular mop of radius R vertically down with a total force F and rotates it with a constant angular speed about its axis. If the force F is distributed uniformly over the mop and if coefficient of friction between the mop and the floor is µ, the torque, applied by the machine on the mop is:
[10 Jan. 2019 I]
Q.136 Correct
Q.136 In-correct
Q.136 Unattempt
A rigid massless rod of length 3l has two masses attached at each end as shown in the figure. The rod is pivoted at point P on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be:

[10 Jan. 2019 II]
A rigid massless rod of length 3l has two masses attached at each end as shown in the figure. The rod is pivoted at point P on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be:

[10 Jan. 2019 II]
Q.137 Correct
Q.137 In-correct
Q.137 Unattempt
An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If AB=BC, and the angle made by AB with downward vertical is theta, then:

[9 Jan. 2019 I]
An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If AB=BC, and the angle made by AB with downward vertical is theta, then:

[9 Jan. 2019 I]
Q.138 Correct
Q.138 In-correct
Q.138 Unattempt
Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10cm and outer radius 20cm), about its axis be 1 . The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also I, is:
[12 Jan. 2019 I]
Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10cm and outer radius 20cm), about its axis be 1 . The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also I, is:
[12 Jan. 2019 I]
Q.139 Correct
Q.139 In-correct
Q.139 Unattempt
The moment of inertia of a solid sphere, about an axis parallel to its diameter and at a distance of x from it, is 'I (x) '. Which one of the graphs represents the variation of I(x) with x correctly?
[12 Jan. 2019 II]
The moment of inertia of a solid sphere, about an axis parallel to its diameter and at a distance of x from it, is 'I (x) '. Which one of the graphs represents the variation of I(x) with x correctly?
[12 Jan. 2019 II]
Q.140 Correct
Q.140 In-correct
Q.140 Unattempt
An equilateral triangle ABC is cut from a thin solid sheet of wood. (See figure) D,E and F are the mid-points of its sides as shown and G is the centre of the triangle. The moment of inertia of the triangle about an axis passing through G and perpendicular to the plane of the triangle is I0. If the smaller triangle DEF is removed from ABC, the moment of inertia of the remaining figure about the same axis is I. Then:

[11 Jan. 2019 I]
An equilateral triangle ABC is cut from a thin solid sheet of wood. (See figure) D,E and F are the mid-points of its sides as shown and G is the centre of the triangle. The moment of inertia of the triangle about an axis passing through G and perpendicular to the plane of the triangle is I0. If the smaller triangle DEF is removed from ABC, the moment of inertia of the remaining figure about the same axis is I. Then:

[11 Jan. 2019 I]
Q.141 Correct
Q.141 In-correct
Q.141 Unattempt
a string is wound around a hollow cylinder of mass 5kg and radius 0.5m. If the string is now pulled with a horizontal force of 40N, and the cylinder is rolling without slipping on a horizontal surface (see figure), then the angular acceleration of the cylinder will be (Neglect the mass and thickness of the string)

[11 Jan. 2019 II]
a string is wound around a hollow cylinder of mass 5kg and radius 0.5m. If the string is now pulled with a horizontal force of 40N, and the cylinder is rolling without slipping on a horizontal surface (see figure), then the angular acceleration of the cylinder will be (Neglect the mass and thickness of the string)

[11 Jan. 2019 II]
Q.142 Correct
Q.142 In-correct
Q.142 Unattempt
A circular disc D1 of mass M and radius R has two identical discs‌D2 and D3 of the same mass M and radius R attached rigidly at its opposite ends (see figure). The moment of inertia of the system about the axis OO', passing through the centre of D1, as shown in the figure, will be :

[11 Jan. 2019 II]
A circular disc D1 of mass M and radius R has two identical discs‌D2 and D3 of the same mass M and radius R attached rigidly at its opposite ends (see figure). The moment of inertia of the system about the axis OO', passing through the centre of D1, as shown in the figure, will be :

[11 Jan. 2019 II]
Q.143 Correct
Q.143 In-correct
Q.143 Unattempt
Two identical spherical balls of mass M and radius R each are stuck on two ends of a rod of length 2R and mass M (see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is:

[10 Jan. 2019 II]
Two identical spherical balls of mass M and radius R each are stuck on two ends of a rod of length 2R and mass M (see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is:

[10 Jan. 2019 II]
Q.144 Correct
Q.144 In-correct
Q.144 Unattempt
Two masses m and
m
2
 are connected at the two ends of a massless rigid rod of length l. The rod is suspended by a thin wire of torsional constant k at the centre of mass of the rod-mass system (see figure). Because of torsional constant k, the restoring toruque is τ=kθ for angular displacement θ. If the rod is rotated by θ0 and released, the tension in it when it passes through its mean position will be:

[9 Jan. 2019 I]
Two masses m and
m
2
 are connected at the two ends of a massless rigid rod of length l. The rod is suspended by a thin wire of torsional constant k at the centre of mass of the rod-mass system (see figure). Because of torsional constant k, the restoring toruque is τ=kθ for angular displacement θ. If the rod is rotated by θ0 and released, the tension in it when it passes through its mean position will be:

[9 Jan. 2019 I]
Q.145 Correct
Q.145 In-correct
Q.145 Unattempt
A rod of length 50cm is pivoted at one end. It is raised such that if makes an angle of 30° from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in rads ‌−1 ) will be (g=10ms−2)

[9 Jan. 2019 II]
A rod of length 50cm is pivoted at one end. It is raised such that if makes an angle of 30° from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in rads ‌−1 ) will be (g=10ms−2)

[9 Jan. 2019 II]
Q.146 Correct
Q.146 In-correct
Q.146 Unattempt
A homogeneous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is:
[10 Jan. 2019 I]
A homogeneous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is:
[10 Jan. 2019 I]
Q.147 Correct
Q.147 In-correct
Q.147 Unattempt
A smooth wire of length 2πr is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed ω about the vertical diameter AB, as shown in figure, the bead is at rest with respect to the circular ring at position P as shown. Then the value of ω2 is equal to :

[12 Apr. 2019 II]
A smooth wire of length 2πr is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed ω about the vertical diameter AB, as shown in figure, the bead is at rest with respect to the circular ring at position P as shown. Then the value of ω2 is equal to :

[12 Apr. 2019 II]
Q.148 Correct
Q.148 In-correct
Q.148 Unattempt
A particle of mass m is moving along a trajectory given by
x=x0+a‌cos‌ω1‌t
y=y0+b‌cos‌ω2‌t
The torque, acting on the particle about the origin, at t=0 is:
[10 Apr. 2019 I]
A particle of mass m is moving along a trajectory given by
x=x0+a‌cos‌ω1‌t
y=y0+b‌cos‌ω2‌t
The torque, acting on the particle about the origin, at t=0 is:
[10 Apr. 2019 I]
Q.149 Correct
Q.149 In-correct
Q.149 Unattempt
The time dependence of the position of a particle of mass m=2 is given by
→
r
(t)=2t
^
i
−3t2
^
j
. Its angular momentum, with respect to the origin, at time t=2 is :
[10 Apr. 2019 II]
The time dependence of the position of a particle of mass m=2 is given by
→
r
(t)=2t
^
i
−3t2
^
j
. Its angular momentum, with respect to the origin, at time t=2 is :
[10 Apr. 2019 II]
Q.150 Correct
Q.150 In-correct
Q.150 Unattempt
A metal coin of mass 5g and radius 1cm is fixed to a thin stick AB of negligible mass as shown in the figure The system is initially at rest. The constant torque, that will make the system rotate about AB at 25 rotations per second in 5s, is close to :

[10 Apr. 2019 II]
A metal coin of mass 5g and radius 1cm is fixed to a thin stick AB of negligible mass as shown in the figure The system is initially at rest. The constant torque, that will make the system rotate about AB at 25 rotations per second in 5s, is close to :

[10 Apr. 2019 II]
Q.151 Correct
Q.151 In-correct
Q.151 Unattempt
A rectangular solid box of length 0.3m is held horizontally, with one of its sides on the edge of a platform of height 5m. When released, it slips off the table in a very short time τ=0.01s, remaining essentially horizontal. The angle by which it would rotate when it hits the ground will be (in radians) close to :

[8 Apr. 2019 II]
A rectangular solid box of length 0.3m is held horizontally, with one of its sides on the edge of a platform of height 5m. When released, it slips off the table in a very short time τ=0.01s, remaining essentially horizontal. The angle by which it would rotate when it hits the ground will be (in radians) close to :

[8 Apr. 2019 II]
Q.152 Correct
Q.152 In-correct
Q.152 Unattempt
A circular disc of radius b has a hole of radius a at its centre (see figure). If the mass per unit area of the disc varies as(
σ0
r
), then the radius of gyration of the disc about its axis passing through the centre is:

[12 Apr. 2019 I]
A circular disc of radius b has a hole of radius a at its centre (see figure). If the mass per unit area of the disc varies as(
σ0
r
), then the radius of gyration of the disc about its axis passing through the centre is:

[12 Apr. 2019 I]
Q.153 Correct
Q.153 In-correct
Q.153 Unattempt
Two coaxial discs, having moments of inertia I1 and
I1
2
, are rotating with respective angular velocities ω1 and
ω1
2
, about their common axis. They are brought in contact with each other and thereafter they rotate with a common angular velocity. If Ef and Ei are the final and initial total energies, then (Ef−Ei) is:
[10 Apr. 2019 I]
Two coaxial discs, having moments of inertia I1 and
I1
2
, are rotating with respective angular velocities ω1 and
ω1
2
, about their common axis. They are brought in contact with each other and thereafter they rotate with a common angular velocity. If Ef and Ei are the final and initial total energies, then (Ef−Ei) is:
[10 Apr. 2019 I]
Q.154 Correct
Q.154 In-correct
Q.154 Unattempt
A thin disc of mass M and radius R has mass per unit area σ(r)=kr2 where r is the distance from its centre. Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane is:
[10 Apr. 2019 I]
A thin disc of mass M and radius R has mass per unit area σ(r)=kr2 where r is the distance from its centre. Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane is:
[10 Apr. 2019 I]
Q.155 Correct
Q.155 In-correct
Q.155 Unattempt
A solid sphere of mass M and radius R is divided into two unequal parts. The first part has a mass of
7M
8
 and is converted into a uniform disc of radius 2R. The second part is converted into a uniform solid sphere. Let I1 be the moment of inertia of the new sphere about its axis. The ratio I1∕I2 is given by:
[10 Apr. 2019 II]
A solid sphere of mass M and radius R is divided into two unequal parts. The first part has a mass of
7M
8
 and is converted into a uniform disc of radius 2R. The second part is converted into a uniform solid sphere. Let I1 be the moment of inertia of the new sphere about its axis. The ratio I1∕I2 is given by:
[10 Apr. 2019 II]
Q.156 Correct
Q.156 In-correct
Q.156 Unattempt
A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of θ, where θ is the angle by which it has rotated, is given as kθ2. If its moment of inertia is I then the angular acceleration of the disc is:
[9 April 2019 I]
A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of θ, where θ is the angle by which it has rotated, is given as kθ2. If its moment of inertia is I then the angular acceleration of the disc is:
[9 April 2019 I]
Q.157 Correct
Q.157 In-correct
Q.157 Unattempt
Moment of inertia of a body about a given axis is 1.5kg m2. Initially the body is at rest. In order to produce a rotational kinetic energy of 1200J, the angular acceleration of 20rad∕s2 must be applied about the axis for a duration of:
[9 Apr. 2019 II]
Moment of inertia of a body about a given axis is 1.5kg m2. Initially the body is at rest. In order to produce a rotational kinetic energy of 1200J, the angular acceleration of 20rad∕s2 must be applied about the axis for a duration of:
[9 Apr. 2019 II]
Q.158 Correct
Q.158 In-correct
Q.158 Unattempt
A thin smooth rod of length L and mass M is rotating freely with angular speed ω0 about an axis perpendicular to the rod and passing through its center. Two beads of mass m and negligible size are at the center of the rod initially. The beads are free to slide along the rod. The angular speed of the system, when the beads reach the opposite ends of the rod, will be:
[9 Apr. 2019 II]
A thin smooth rod of length L and mass M is rotating freely with angular speed ω0 about an axis perpendicular to the rod and passing through its center. Two beads of mass m and negligible size are at the center of the rod initially. The beads are free to slide along the rod. The angular speed of the system, when the beads reach the opposite ends of the rod, will be:
[9 Apr. 2019 II]
Q.159 Correct
Q.159 In-correct
Q.159 Unattempt
A thin circular plate of mass M and radius R has its density varying as ρ(r)=ρ0r with ρ0 as constant and r is the distance from its center. The moment of Inertia of the circular plate about an axis perpendicular to the plate and passing through its edge is I=aMR2. The value of the coefficient a is:
[8 April 2019 I]
A thin circular plate of mass M and radius R has its density varying as ρ(r)=ρ0r with ρ0 as constant and r is the distance from its center. The moment of Inertia of the circular plate about an axis perpendicular to the plate and passing through its edge is I=aMR2. The value of the coefficient a is:
[8 April 2019 I]
Q.160 Correct
Q.160 In-correct
Q.160 Unattempt
A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights hsph and hcyl on the incline. The ratio
hsph
hcyl
 is given by:

[8 Apr. 2019 II]
A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights hsph and hcyl on the incline. The ratio
hsph
hcyl
 is given by:

[8 Apr. 2019 II]
Q.161 Correct
Q.161 In-correct
Q.161 Unattempt
The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal plane:
(i) a ring of radius R(ii) a solid cylinder of radius
R
2
and (iii) a solid sphere of radius
R
4
. If, in each case, thespeed of the center of mass at the bottom of the incline is same, the ratio of the maximum heights they climb is:
[9 April 2019 I]
The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal plane:
(i) a ring of radius R(ii) a solid cylinder of radius
R
2
and (iii) a solid sphere of radius
R
4
. If, in each case, thespeed of the center of mass at the bottom of the incline is same, the ratio of the maximum heights they climb is:
[9 April 2019 I]
Q.162 Correct
Q.162 In-correct
Q.162 Unattempt
Three particles of masses 50g,100g and 150g are placed at the vertices of an equilateral triangle of side 1m (as shown in the figure). The (x,y) coordinates of the centre of mass will be :

[12 Apr. 2019 II]
Three particles of masses 50g,100g and 150g are placed at the vertices of an equilateral triangle of side 1m (as shown in the figure). The (x,y) coordinates of the centre of mass will be :

[12 Apr. 2019 II]
Q.163 Correct
Q.163 In-correct
Q.163 Unattempt
Four particles A,B,C and D with masses mA=m,mB=2m,mC=3m and mD=4m are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is :

[8 April 2019 I]
Four particles A,B,C and D with masses mA=m,mB=2m,mC=3m and mD=4m are at the corners of a square.They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is :

[8 April 2019 I]
Q.164 Correct
Q.164 In-correct
Q.164 Unattempt
A uniform rectangular thin sheet ABCD of mass M has length a and breadth b, as shown in the figure. If the shaded portion HBGO is cut-off, the coordinates of the centre of mass of the remaining portion will be :

[8 Apr. 2019 II]
A uniform rectangular thin sheet ABCD of mass M has length a and breadth b, as shown in the figure. If the shaded portion HBGO is cut-off, the coordinates of the centre of mass of the remaining portion will be :

[8 Apr. 2019 II]
Q.165 Correct
Q.165 In-correct
Q.165 Unattempt
A uniform rod of length l is being rotated in a horizontal plane with a constant angular speed about an axis passing through one of its ends. If the tension generated in the rod due to rotation is T(x) at a distance x from the axis, then which of the following graphs depicts it most closely?
[12 Apr. 2019 II]
A uniform rod of length l is being rotated in a horizontal plane with a constant angular speed about an axis passing through one of its ends. If the tension generated in the rod due to rotation is T(x) at a distance x from the axis, then which of the following graphs depicts it most closely?
[12 Apr. 2019 II]
Q.166 Correct
Q.166 In-correct
Q.166 Unattempt
A force of 40N acts on a point B at the end of an L -shaped object, as shown in the figure. The angle θ that will produce maximum moment of the force about point A is given by:

[Online April 15, 2018]
A force of 40N acts on a point B at the end of an L -shaped object, as shown in the figure. The angle θ that will produce maximum moment of the force about point A is given by:

[Online April 15, 2018]
Q.167 Correct
Q.167 In-correct
Q.167 Unattempt
A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the nth power of R. If the period of rotation of the particle is T, then:
[2018]
A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the nth power of R. If the period of rotation of the particle is T, then:
[2018]
Q.168 Correct
Q.168 In-correct
Q.168 Unattempt
A uniform rod‌A‌B is suspended from a point X, at a variable distance from x from A, as shown. To make the rod horizontal, a mass m is suspended from its end A. A set of (m,x) values is recorded. The appropriate variable that give a straight line, when plotted, are:
[Online April 15, 2018]

A uniform rod‌A‌B is suspended from a point X, at a variable distance from x from A, as shown. To make the rod horizontal, a mass m is suspended from its end A. A set of (m,x) values is recorded. The appropriate variable that give a straight line, when plotted, are:
[Online April 15, 2018]
Q.169 Correct
Q.169 In-correct
Q.169 Unattempt
A thin uniform bar of length L and mass 8m lies on a smooth horizontal table. Two point masses m and 2m moving in the same horizontal plane from opposite sides of the bar with speeds 2v and v respectively. The masses stick to the bar after collision at a distance
L
3
 and
L
6
 respectively from the centre of the bar. If the bar starts rotating about its center of mass as a result of collision, the angular speed of the bar will be:

[Online April 15, 2018]
A thin uniform bar of length L and mass 8m lies on a smooth horizontal table. Two point masses m and 2m moving in the same horizontal plane from opposite sides of the bar with speeds 2v and v respectively. The masses stick to the bar after collision at a distance
L
3
 and
L
6
 respectively from the centre of the bar. If the bar starts rotating about its center of mass as a result of collision, the angular speed of the bar will be:

[Online April 15, 2018]
Q.170 Correct
Q.170 In-correct
Q.170 Unattempt
Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is:

[2018]
Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is:

[2018]
Q.171 Correct
Q.171 In-correct
Q.171 Unattempt
From a uniform circular disc of radius R and mass 9M,asmall disc of radius
R
3
 is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing, through centre of disc is :

[2018]
From a uniform circular disc of radius R and mass 9M,asmall disc of radius
R
3
 is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing, through centre of disc is :

[2018]
Q.172 Correct
Q.172 In-correct
Q.172 Unattempt
A thin circular disk is in the xy plane as shown in the figure. The ratio of its moment of inertia about z and z′ axes will be

[Online April 16, 2018]
A thin circular disk is in the xy plane as shown in the figure. The ratio of its moment of inertia about z and z′ axes will be


[Online April 16, 2018]
Q.173 Correct
Q.173 In-correct
Q.173 Unattempt
A thin rod‌MN, free to rotate in the vertical plane about the fixed end N, is held horizontal. When the end M is released the speed of this end, when the rod makes an angle α with the horizontal, will be proportional to: (see figure)

[Online April 15, 2018]
A thin rod‌MN, free to rotate in the vertical plane about the fixed end N, is held horizontal. When the end M is released the speed of this end, when the rod makes an angle α with the horizontal, will be proportional to: (see figure)

[Online April 15, 2018]
Q.174 Correct
Q.174 In-correct
Q.174 Unattempt
In a physical balance working on the principle of moments, when 5mg weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?
[Online April 8, 2017]
In a physical balance working on the principle of moments, when 5mg weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?
[Online April 8, 2017]
Q.175 Correct
Q.175 In-correct
Q.175 Unattempt
The machine as shown has 2 rods of length 1m connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has a roller that rolls along the floor in a slot.
As the roller goes back and forth, a 2kg weight moves up and down. If the roller is moving towards right at a constant speed, the weight moves up with a :

[Online April 9, 2017]
The machine as shown has 2 rods of length 1m connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has a roller that rolls along the floor in a slot.
As the roller goes back and forth, a 2kg weight moves up and down. If the roller is moving towards right at a constant speed, the weight moves up with a :

[Online April 9, 2017]
Q.176 Correct
Q.176 In-correct
Q.176 Unattempt
A slender uniform rod of mass M and length ell is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle θ with the vertical is

[2017]
A slender uniform rod of mass M and length ell is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle θ with the vertical is

[2017]
Q.177 Correct
Q.177 In-correct
Q.177 Unattempt
The moment of inertia of a uniform cylinder of length l and radius R about its perpendicular bisector is I. What is the ratio l∕R such that the moment of inertia is minimum?
[2017]
The moment of inertia of a uniform cylinder of length l and radius R about its perpendicular bisector is I. What is the ratio l∕R such that the moment of inertia is minimum?
[2017]
Q.178 Correct
Q.178 In-correct
Q.178 Unattempt
Moment of inertia of an equilateral triangular lamina ABC, about the axis passing through its centre O and perpendicular to its plane is I0 as shown in the figure. A cavity DEF is cut out from the lamina, where D,E,F are the mid points of the sides. Moment of inertia of the remaining part of lamina about the same axis is:

[Online April 8, 2017]
Moment of inertia of an equilateral triangular lamina ABC, about the axis passing through its centre O and perpendicular to its plane is I0 as shown in the figure. A cavity DEF is cut out from the lamina, where D,E,F are the mid points of the sides. Moment of inertia of the remaining part of lamina about the same axis is:

[Online April 8, 2017]
Q.179 Correct
Q.179 In-correct
Q.179 Unattempt
A circular hole of radius
R
4
 is made in a thin uniform disc having mass M and radius R, as shown in figure. The moment of inertia of the remaining portion of the disc about an axis passing through the point O and perpendicular to the plane of the disc is :

[Online April 9, 2017]
A circular hole of radius
R
4
 is made in a thin uniform disc having mass M and radius R, as shown in figure. The moment of inertia of the remaining portion of the disc about an axis passing through the point O and perpendicular to the plane of the disc is :

[Online April 9, 2017]
Q.180 Correct
Q.180 In-correct
Q.180 Unattempt
In the figure shown ABC is a uniform wire. If centre of mass of wire lies vertically below point A, then
BC
AB
 is close to :

[Online April 10, 2016]
In the figure shown ABC is a uniform wire. If centre of mass of wire lies vertically below point A, then
BC
AB
 is close to :

[Online April 10, 2016]
Q.181 Correct
Q.181 In-correct
Q.181 Unattempt
Concrete mixture is made by mixing cement, stone and sand in a rotating cylindrical drum. If the drum rotates too fast, the ingredients remain stuck to the wall of the drum and proper mixing of ingredients does not take place. The maximum rotational speed of the drum in revolutions per minute (rpm) to ensure proper mixing is close to :
(Take the radius of the drum to be 1.25m and its axle to be horizontal):
[Online April 10, 2016]
Concrete mixture is made by mixing cement, stone and sand in a rotating cylindrical drum. If the drum rotates too fast, the ingredients remain stuck to the wall of the drum and proper mixing of ingredients does not take place. The maximum rotational speed of the drum in revolutions per minute (rpm) to ensure proper mixing is close to :
(Take the radius of the drum to be 1.25m and its axle to be horizontal):
[Online April 10, 2016]
Q.182 Correct
Q.182 In-correct
Q.182 Unattempt
A cubical block of side 30cm is moving with velocity 2ms−1 on a smooth horizontal surface. The surface has a bump at a point O as shown in figure. The angular velocity (in rad∕s ) of the block immediately after it hits the bump, is:

[Online April 9, 2016]
A cubical block of side 30cm is moving with velocity 2ms−1 on a smooth horizontal surface. The surface has a bump at a point O as shown in figure. The angular velocity (in rad∕s ) of the block immediately after it hits the bump, is:

[Online April 9, 2016]
Q.183 Correct
Q.183 In-correct
Q.183 Unattempt
A particle of mass m is moving along the side of a square of side ′a′, with a uniform speed v in the x−y plane as shown in the figure:
Which of the following statements is false for the angular momentum
→
L
 about the origin?
[2016]
A particle of mass m is moving along the side of a square of side ′a′, with a uniform speed v in the x−y plane as shown in the figure:

Which of the following statements is false for the angular momentum
→
L
 about the origin?
[2016]
Q.184 Correct
Q.184 In-correct
Q.184 Unattempt
A roller is made by joining together two cones at their vertices O. It is kept on two rails AB and CD, which are placed asymmetrically (see figure), with its axis perpendicular to CD and its centre O at the centre of line joining AB and Cd (see figure). It is given a light push so that it starts rolling with its centre O moving parallel to CD in the direction shown. As it moves, the roller will tend to:

[2016]
A roller is made by joining together two cones at their vertices O. It is kept on two rails AB and CD, which are placed asymmetrically (see figure), with its axis perpendicular to CD and its centre O at the centre of line joining AB and Cd (see figure). It is given a light push so that it starts rolling with its centre O moving parallel to CD in the direction shown. As it moves, the roller will tend to:

[2016]
Q.185 Correct
Q.185 In-correct
Q.185 Unattempt
Distance of the centre of mass of a solid uniform cone from its vertex is z0. If the radius of its base is R and its height is h then z0 is equal to :
[2015]
Distance of the centre of mass of a solid uniform cone from its vertex is z0. If the radius of its base is R and its height is h then z0 is equal to :
[2015]
Q.186 Correct
Q.186 In-correct
Q.186 Unattempt
A uniform thin rod AB of length L has linear mass density µ(x)=a+
bx
L
, where x is measured from A. If the CM of the rod lies at a distance of (
7
12
)L from A, then a and b are related as :
[Online April 11, 2015]
A uniform thin rod AB of length L has linear mass density µ(x)=a+
bx
L
, where x is measured from A. If the CM of the rod lies at a distance of (
7
12
)L from A, then a and b are related as :
[Online April 11, 2015]
Q.187 Correct
Q.187 In-correct
Q.187 Unattempt
A particle of mass 2kg is on a smooth horizontal table and moves in a circular path of radius 0.6m. The height of the table from the ground is 0.8m. If the angular speed of the particle is 12rads−1, the magnitude of its angular momentum about a point on the ground right under the centre of the circle is:
[Online April 11, 2015]
A particle of mass 2kg is on a smooth horizontal table and moves in a circular path of radius 0.6m. The height of the table from the ground is 0.8m. If the angular speed of the particle is 12rads−1, the magnitude of its angular momentum about a point on the ground right under the centre of the circle is:
[Online April 11, 2015]
Q.188 Correct
Q.188 In-correct
Q.188 Unattempt
From a solid sphere of mass M and radius R a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its center and perpendicular to one of its faces is:
[2015]
From a solid sphere of mass M and radius R a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its center and perpendicular to one of its faces is:
[2015]
Q.189 Correct
Q.189 In-correct
Q.189 Unattempt
Consider a thin uniform square sheet made of a rigid material. If its side is ' a ' mass m and moment of inertia I about one of its diagonals, then :
[Online April 10, 2015]
Consider a thin uniform square sheet made of a rigid material. If its side is ' a ' mass m and moment of inertia I about one of its diagonals, then :
[Online April 10, 2015]
Q.190 Correct
Q.190 In-correct
Q.190 Unattempt
A uniform solid cylindrical roller of mass ' m ' is being pulled on a horizontal surface with force F parallel to the surface and applied at its centre. If the acceleration of the cylinder is 'a' and it is rolling without slipping then the value of 'F' is:
[Online April 10, 2015]
A uniform solid cylindrical roller of mass ' m ' is being pulled on a horizontal surface with force F parallel to the surface and applied at its centre. If the acceleration of the cylinder is 'a' and it is rolling without slipping then the value of 'F' is:
[Online April 10, 2015]
Q.191 Correct
Q.191 In-correct
Q.191 Unattempt
A thin bar of length L has a mass per unit length lambda, that increases linearly with distance from one end. If its total mass is M and its mass per unit length at the lighter end is λo, then the distance of the centre of mass from the lighter end is:
[Online April 11, 2014]
A thin bar of length L has a mass per unit length lambda, that increases linearly with distance from one end. If its total mass is M and its mass per unit length at the lighter end is λo, then the distance of the centre of mass from the lighter end is:
[Online April 11, 2014]
Q.192 Correct
Q.192 In-correct
Q.192 Unattempt
A bob of mass m attached to an inextensible string of length l is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed w rad/s about the vertical. About the point of suspension:
[2014]
A bob of mass m attached to an inextensible string of length l is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed w rad/s about the vertical. About the point of suspension:
[2014]
Q.193 Correct
Q.193 In-correct
Q.193 Unattempt
A ball of mass 160 g is thrown up at an angle of 60° to the horizontal at a speed of 10 ms‌–1. The angular momentum of the ball at the highest point of the trajectory with respect to the point from which the ball is thrown is nearly (g = 10 ms–2)
[Online April 19, 2014]
A ball of mass 160 g is thrown up at an angle of 60° to the horizontal at a speed of 10 ms‌–1. The angular momentum of the ball at the highest point of the trajectory with respect to the point from which the ball is thrown is nearly (g = 10 ms–2)
[Online April 19, 2014]
Q.194 Correct
Q.194 In-correct
Q.194 Unattempt
A particle is moving in a circular path of radius a, with a constant velocity v as shown in the figure. The centre of circle is marked by ‘C’. The angular momentum from the origin O can be written as:

[Online April 12, 2014]
A particle is moving in a circular path of radius a, with a constant velocity v as shown in the figure. The centre of circle is marked by ‘C’. The angular momentum from the origin O can be written as:

[Online April 12, 2014]
Q.195 Correct
Q.195 In-correct
Q.195 Unattempt
A cylinder of mass Mc and sphere of mass Ms are placed at points A and B of two inclines, respectively (See Figure). If they roll on the incline without slipping such that their accelerations are the same, then the ratio
sin‌θc
sin‌θs
 is:

[Online April 9, 2014]
A cylinder of mass Mc and sphere of mass Ms are placed at points A and B of two inclines, respectively (See Figure). If they roll on the incline without slipping such that their accelerations are the same, then the ratio
sin‌θc
sin‌θs
 is:

[Online April 9, 2014]
Q.196 Correct
Q.196 In-correct
Q.196 Unattempt
A boy of mass 20 kg is standing on a 80 kg free to move long cart. There is negligible friction between cart and ground. Initially, the boy is standing 25 m from a wall. If he walks 10 m on the cart towards the wall, then the final distance of the boy from the wall will be
[Online April 23, 2013]
A boy of mass 20 kg is standing on a 80 kg free to move long cart. There is negligible friction between cart and ground. Initially, the boy is standing 25 m from a wall. If he walks 10 m on the cart towards the wall, then the final distance of the boy from the wall will be
[Online April 23, 2013]
Q.197 Correct
Q.197 In-correct
Q.197 Unattempt
A particle of mass 2kg is moving such that at time t, its position, in meter, is given by
→
r
(t)=5
^
i
−2t2
^
j
. The angular momentum of the particle at t=2s about the origin in kgm−2s−1 is :
[Online April 23, 2013]
A particle of mass 2kg is moving such that at time t, its position, in meter, is given by
→
r
(t)=5
^
i
−2t2
^
j
. The angular momentum of the particle at t=2s about the origin in kgm−2s−1 is :
[Online April 23, 2013]
Q.198 Correct
Q.198 In-correct
Q.198 Unattempt
A bullet of mass 10 g and speed 500 m/s is fired into a door and gets embedded exactly at the centre of the door. The door is 1.0 m wide and weighs 12 kg. It is hinged at one end and rotates about a vertical axis practically without friction.
The angular speed of the door just after the bullet embeds into it will be :
[Online April 9, 2013]
A bullet of mass 10 g and speed 500 m/s is fired into a door and gets embedded exactly at the centre of the door. The door is 1.0 m wide and weighs 12 kg. It is hinged at one end and rotates about a vertical axis practically without friction.
The angular speed of the door just after the bullet embeds into it will be :
[Online April 9, 2013]
Q.199 Correct
Q.199 In-correct
Q.199 Unattempt
A ring of mass M and radius R is rotating about its axis with angular velocity ω. Two identical bodies each of mass m are now gently attached at the two ends of a diameter of the ring. Because of this, the kinetic energy loss will be:
[Online April 25, 2013]
A ring of mass M and radius R is rotating about its axis with angular velocity ω. Two identical bodies each of mass m are now gently attached at the two ends of a diameter of the ring. Because of this, the kinetic energy loss will be:
[Online April 25, 2013]
Q.200 Correct
Q.200 In-correct
Q.200 Unattempt
A loop of radius r and mass m rotating with an angular velocity ω0 is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?
[2013]
A loop of radius r and mass m rotating with an angular velocity ω0 is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?
[2013]
Q.201 Correct
Q.201 In-correct
Q.201 Unattempt
A tennis ball (treated as hollow spherical shell) starting from O rolls down a hill. At point A the ball becomes air borne leaving at an angle of 30° with the horizontal. The ball strikes the ground at B. What is the value of the distance AB?
(Moment of inertia of a spherical shell of mass m and radius R about its diameter =
2
3
mR2 )

[Online April 22, 2013]
A tennis ball (treated as hollow spherical shell) starting from O rolls down a hill. At point A the ball becomes air borne leaving at an angle of 30° with the horizontal. The ball strikes the ground at B. What is the value of the distance AB?
(Moment of inertia of a spherical shell of mass m and radius R about its diameter =
2
3
mR2 )

[Online April 22, 2013]
Q.202 Correct
Q.202 In-correct
Q.202 Unattempt
Two point masses of mass m1=fM and m2=(1−f)M(f <1 ) are in outer space (far from gravitational influence of other objects) at a distance R from each other. They move in circular orbits about their centre of mass with angular velocities ω1 for m1 and ω2 for m2. In that case
[Online May 19, 2012]
Two point masses of mass m1=fM and m2=(1−f)M(f <1 ) are in outer space (far from gravitational influence of other objects) at a distance R from each other. They move in circular orbits about their centre of mass with angular velocities ω1 for m1 and ω2 for m2. In that case
[Online May 19, 2012]
Q.203 Correct
Q.203 In-correct
Q.203 Unattempt
A stone of mass m, tied to the end of a string, is whirled around in a circle on a horizontal frictionless table. The length of the string is reduced gradually keeping the angular momentum of the stone about the centre of the circle constant. Then, the tension in the string is given by T=Arn , where A is a constant, r is the instantaneous radius of the circle. The value of n is equal to
[Online May 26, 2012]
A stone of mass m, tied to the end of a string, is whirled around in a circle on a horizontal frictionless table. The length of the string is reduced gradually keeping the angular momentum of the stone about the centre of the circle constant. Then, the tension in the string is given by T=Arn , where A is a constant, r is the instantaneous radius of the circle. The value of n is equal to
[Online May 26, 2012]
Q.204 Correct
Q.204 In-correct
Q.204 Unattempt
This question has Statement land Statement 2 . Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement 1: When moment of inertia I of a body rotating about an axis with angular speed ω increases, its angular momentum L is unchanged but the kinetic energy K increases if there is no torque applied on it.
Statement 2: L=Iω, kinetic energy of rotation =
1
2
Iω2
[Online May 12, 2012]
This question has Statement land Statement 2 . Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement 1: When moment of inertia I of a body rotating about an axis with angular speed ω increases, its angular momentum L is unchanged but the kinetic energy K increases if there is no torque applied on it.
Statement 2: L=Iω, kinetic energy of rotation =
1
2
Iω2
[Online May 12, 2012]
Q.205 Correct
Q.205 In-correct
Q.205 Unattempt
A solid sphere having mass m and radius r rolls down an inclined plane. Then its kinetic energy is
[Online May 7, 2012]
A solid sphere having mass m and radius r rolls down an inclined plane. Then its kinetic energy is
[Online May 7, 2012]
Q.206 Correct
Q.206 In-correct
Q.206 Unattempt
A circular hole of diameter R is cut from a disc of mass‌M and radius R; the circumference of the cut passes through the centre of the disc. The moment of inertia of the remaining portion of the disc about an axis perpendicular to the disc and passing through its centre is
[Online May 7, 2012]
A circular hole of diameter R is cut from a disc of mass‌M and radius R; the circumference of the cut passes through the centre of the disc. The moment of inertia of the remaining portion of the disc about an axis perpendicular to the disc and passing through its centre is
[Online May 7, 2012]
Q.207 Correct
Q.207 In-correct
Q.207 Unattempt
A thick-walled hollow sphere has outside radius R0. It rolls down an incline without slipping and its speed at the bottom is v0. Now the incline is waxed, so that it is practically frictionless and the sphere is observed to slide down (without any rolling). Its speed at the bottom is observed to be 5v0∕4. The radius of gyration of the hollow sphere about an axis through its centre is
[Online May 26, 2012]
A thick-walled hollow sphere has outside radius R0. It rolls down an incline without slipping and its speed at the bottom is v0. Now the incline is waxed, so that it is practically frictionless and the sphere is observed to slide down (without any rolling). Its speed at the bottom is observed to be 5v0∕4. The radius of gyration of the hollow sphere about an axis through its centre is
[Online May 26, 2012]
Q.208 Correct
Q.208 In-correct
Q.208 Unattempt
A solid sphere is rolling on a surface as shown in figure, with a translational velocity vms−1. If it is to climb the inclined surface continuing to roll without slipping, then minimum velocity for this to happen is

[Online May 12, 2012]
A solid sphere is rolling on a surface as shown in figure, with a translational velocity vms−1. If it is to climb the inclined surface continuing to roll without slipping, then minimum velocity for this to happen is

[Online May 12, 2012]
Q.209 Correct
Q.209 In-correct
Q.209 Unattempt
A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc.
[2011]
A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc.
[2011]
Q.210 Correct
Q.210 In-correct
Q.210 Unattempt
A mass m hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass m and radius R. Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass m, if the string does not slip on the pulley, is:
[2011]
A mass m hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass m and radius R. Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass m, if the string does not slip on the pulley, is:
[2011]
Q.211 Correct
Q.211 In-correct
Q.211 Unattempt
A pulley of radius 2m is rotated about its axis by a force F=(20t−5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10kg−m2 the number of rotations made by the pulley before its direction of motion is reversed, is:
[2011]
A pulley of radius 2m is rotated about its axis by a force F=(20t−5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10kg−m2 the number of rotations made by the pulley before its direction of motion is reversed, is:
[2011]
Q.212 Correct
Q.212 In-correct
Q.212 Unattempt
A small particle of mass m is projected at an angle θ with the x -axis with an initial velocity v0 in the x -y plane as shown in the figure. At a time t<
v0‌sin‌θ
g
, the angular momentum of the particle is

[2010]
A small particle of mass m is projected at an angle θ with the x -axis with an initial velocity v0 in the x -y plane as shown in the figure. At a time t<
v0‌sin‌θ
g
, the angular momentum of the particle is

[2010]
Q.213 Correct
Q.213 In-correct
Q.213 Unattempt
A thin uniform rod of length l and mass m is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is ω. Its centre of mass rises to a maximum height of
[2009]
A thin uniform rod of length l and mass m is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is ω. Its centre of mass rises to a maximum height of
[2009]
Q.214 Correct
Q.214 In-correct
Q.214 Unattempt
A thin rod of length ' L ' is lying along the x -axis with its ends at x=0 and x=L. Its linear density (mass/length) varies with x as k(
x
L
)n, where n can be zero or any positive number. If the position xCM of the centre of mass of the rod is plotted against ' n, which of the following graphs best approximates the dependence of xCM on n ?
[2008]
A thin rod of length ' L ' is lying along the x -axis with its ends at x=0 and x=L. Its linear density (mass/length) varies with x as k(
x
L
)n, where n can be zero or any positive number. If the position xCM of the centre of mass of the rod is plotted against ' n, which of the following graphs best approximates the dependence of xCM on n ?
[2008]
Q.215 Correct
Q.215 In-correct
Q.215 Unattempt
Consider a uniform square plate of side ' a ' and mass ' M ' The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is
[2008]
Consider a uniform square plate of side ' a ' and mass ' M ' The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is
[2008]
Q.216 Correct
Q.216 In-correct
Q.216 Unattempt
A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is α/R form the centre of the bigger disc. The value of α is
[2007]
A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is α/R form the centre of the bigger disc. The value of α is
[2007]
Q.217 Correct
Q.217 In-correct
Q.217 Unattempt
Angular momentum of the particle rotating with a central force is constant due to
[2007]
Angular momentum of the particle rotating with a central force is constant due to
[2007]
Q.218 Correct
Q.218 In-correct
Q.218 Unattempt
For the given uniform square lamina ABCD, whose centre is O
[2007]
For the given uniform square lamina ABCD, whose centre is O
[2007]
Q.219 Correct
Q.219 In-correct
Q.219 Unattempt
A round uniform body of radius R, mass M and moment of inertia I rolls down (without slipping) an inclined plane making an angle θ with the horizontal. Then its acceleration is
[2007]
A round uniform body of radius R, mass M and moment of inertia I rolls down (without slipping) an inclined plane making an angle θ with the horizontal. Then its acceleration is
[2007]
Q.220 Correct
Q.220 In-correct
Q.220 Unattempt
Consider a two particle system with particles having masses m1 and m2. If the first particle is pushed towards the centre of mass through a distance d, by what distance should the second particle is moved, so as to keep the centre of mass at the same position?
[2006]
Consider a two particle system with particles having masses m1 and m2. If the first particle is pushed towards the centre of mass through a distance d, by what distance should the second particle is moved, so as to keep the centre of mass at the same position?
[2006]
Q.221 Correct
Q.221 In-correct
Q.221 Unattempt
A thin circular ring of mass m and radius R is rotating about its axis with a constant angular velocity ω. Two objects each of mass M are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity ω' =
[2006]
A thin circular ring of mass m and radius R is rotating about its axis with a constant angular velocity ω. Two objects each of mass M are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity ω' =
[2006]
Q.222 Correct
Q.222 In-correct
Q.222 Unattempt
A force of −F
^
k
 acts on O, the origin of the coordinate system. The torque about the point (1, –1) is

[2006]
A force of −F
^
k
 acts on O, the origin of the coordinate system. The torque about the point (1, –1) is

[2006]
Q.223 Correct
Q.223 In-correct
Q.223 Unattempt
Four point masses, each of value m, are placed at the corners of a square ABCD of side l. The moment of inertia of this system about an axis passing through A and parallel to BD is
[2006]
Four point masses, each of value m, are placed at the corners of a square ABCD of side l. The moment of inertia of this system about an axis passing through A and parallel to BD is
[2006]
Q.224 Correct
Q.224 In-correct
Q.224 Unattempt
A body A of mass M while falling vertically downwards under gravity breaks into two parts; a body B of mass
1
3
 M and a body C of mass
2
3
M. The centre of mass of bodies B and C taken together shifts compared to that of body A towards
[2005]
A body A of mass M while falling vertically downwards under gravity breaks into two parts; a body B of mass
1
3
 M and a body C of mass
2
3
M. The centre of mass of bodies B and C taken together shifts compared to that of body A towards
[2005]
Q.225 Correct
Q.225 In-correct
Q.225 Unattempt
A ' T shaped object with dimensions shown in the figure is lying on a smooth floor. A force '
→
F
 ' is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the location of P with respect to C.

[2005]
A ' T shaped object with dimensions shown in the figure,is lying on a smooth floor. A force '
→
F
 ' is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the location of P with respect to C.

[2005]
Q.226 Correct
Q.226 In-correct
Q.226 Unattempt
The moment of inertia of a uniform semicircular disc of mass M and radius r about a line perpendicular to the plane of the disc through the centre is
[2005]
The moment of inertia of a uniform semicircular disc of mass M and radius r about a line perpendicular to the plane of the disc through the centre is
[2005]
Q.227 Correct
Q.227 In-correct
Q.227 Unattempt
A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same, which one of the following will not be affected ?
[2004]
A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same, which one of the following will not be affected ?
[2004]
Q.228 Correct
Q.228 In-correct
Q.228 Unattempt
One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moment of inertia about their diameters are respectively IA and IB Such that
[2004]
One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moment of inertia about their diameters are respectively IA and IB Such that
[2004]
Q.229 Correct
Q.229 In-correct
Q.229 Unattempt
Let
→
F
 be the force acting on a particle having position vector
→
r
, and
→
T
 be the torque of this force about the origin. Then
[2003]
Let
→
F
 be the force acting on a particle having position vector
→
r
, and
→
T
 be the torque of this force about the origin. Then
[2003]
Q.230 Correct
Q.230 In-correct
Q.230 Unattempt
A circular disc X of radius R is made from an iron plate of thickness t, and another disc Y of radius 4R is made from an iron plate of thickness
t
4
. Then the relation between the moment of inertia IX and II is
[2003]
A circular disc X of radius R is made from an iron plate of thickness t, and another disc Y of radius 4R is made from an iron plate of thickness
t
4
. Then the relation between the moment of inertia IX and II is
[2003]
Q.231 Correct
Q.231 In-correct
Q.231 Unattempt
A particle performing uniform circular motion has angular frequency is doubled & its kinetic energy halved, then the new angular momentum is
[2003]
A particle performing uniform circular motion has angular frequency is doubled & its kinetic energy halved, then the new angular momentum is
[2003]
Q.232 Correct
Q.232 In-correct
Q.232 Unattempt
A particle of mass m moves along line PC with velocity v as shown. What is the angular momentum of the particle about P?

[2002]
A particle of mass m moves along line PC with velocity v as shown. What is the angular momentum of the particle about P?

[2002]
Q.233 Correct
Q.233 In-correct
Q.233 Unattempt
Moment of inertia of a circular wire of mass M and radius R about its diameter is
[2002]
Moment of inertia of a circular wire of mass M and radius R about its diameter is
[2002]
Q.234 Correct
Q.234 In-correct
Q.234 Unattempt
Initial angular velocity of a circular disc of mass M is ω1. Then two small spheres of mass m are attached gently to diametrically opposite points on the edge of the disc. What is the final angular velocity of the disc?
[2002]
Initial angular velocity of a circular disc of mass M is ω1. Then two small spheres of mass m are attached gently to diametrically opposite points on the edge of the disc. What is the final angular velocity of the disc?
[2002]
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