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Read the assertion and reason carefully to mark the correct option out of the options given below:
Assertion: Smaller the orbit of the planet around the sun, shorter is the time it takes to complete one revolution.
Reason: According to Kepler’s third law of planetary motion, square of time period is proportional to cube of mean distance from sun.
According to Kepler’s third law T2 ∝ r3 If r is small then T will also be small.
Assertion: Gravitational force between two particles is negligibly small compared to the electrical force.
Reason: The electrical force is experienced by charged particles only.
For two electron Fg/Fe = 10-43 i.e. gravitational force is negligible in comparison to electrostatic force of attraction.
Assertion: The universal gravitational constant is same as acceleration due to gravity. Reason: Gravitational constant and acceleration due to gravity have same dimensional formula.
The universal gravitational constant G is totally different from g.
The constant G is scalar and posses the dimensions [M−1L3T−2]
g is a vector and has got the dimensions [M0LT−2]. It is not a universal constant.
Assertion: If a pendulum is suspended in a lift and lift is falling freely, then its time period becomes infinite.
Reason: Free falling body has acceleration equal to acceleration due to gravity.
If a pendulum is suspended in a lift and lift is moving downward with some acceleration a, then time period of pendulum is given by,
In the case of free fall, a=g then T=∞ i.e The time period of the pendulum becomes infinite.
Assertion: If earth suddenly stops rotating about its axis, then the value of acceleration due to gravity will become the same at all the places.
Reason: The value of acceleration due to gravity is independent of rotation of earth.
The value of g at any place is given by the relation, g′ = g − ω2Recos2λ When l is angle of latitude and w is the angular velocity of earth. If earth suddenly stops rotating, then ω = 0 \ g′ = g i.e., the value of g will be the same at all places.
Assertion: There is no effect of rotation of earth on acceleration due to gravity at poles.
Reason: Rotation of earth is about the polar axis.
As the rotation of earth takes place about polar axis therefore body placed at poles will not feel any centrifugal force and its weight or acceleration due to gravity remains unaffected.
Assertion: A force act upon the earth revolving in a circular orbit about the sun. Hence work should be done on the earth.
Reason: The necessary centripetal force for circular motion of earth comes from the gravitational force between earth and sun.
Earth revolves around the sun in circular path and required centripetal force is provided by gravitational force between earth and sun but the work done by this centripetal force is zero.
Assertion: The ratio of inertial mass to gravitational mass is equal to one.
Reason: The inertial mass and gravitational mass of a body are equivalent.
Inertial mass and gravitational mass are equivalent. Both are scaler quanties and measured in the same unit. They are quite different in the method of their measurement. Also gravitational mass of a body is affected by the presence of other bodies near it whereas internal mass remain unaffected.
Assertion: Gravitational potential of earth at every place on it is negative.
Reason: Everybody on earth is bound by the attraction of earth.
Because gravitational force is always attractive in nature and every body is bound by this gravitational force of attraction of earth.
Assertion: A planet moves faster, when it is closer to the sun in its orbit and vice versa.
Reason: Orbital velocity in orbital of planet is constant.
According to Kepler?s law of planetary motion, a planet revolves around the sun in such a way that its areal velocity is constant. i.e., it move faster, when it is closer the sun and vice-versa.
Assertion: If an earth satellite moves to a lower orbit, there is some dissipation of energy but the satellite speed increases.
Reason: The speed of satellite is a constant quantity.
Due to resistance force of atmosphere, the satellite revolving around the earth losses kinetic energy. Therefore in a particular orbit the gravitational attraction of earth on satellite becomes greater than that required for circular orbit there. Therefore satellite moves down to a lower orbit. In the lower orbit as the potential energy(U=−GMm/r)becomes more negative, Hence kinetic energy (EK=GMm/2r) increases, and hence speed of satellite increases.
Assertion: Earth has an atmosphere but the moon does not.
Reason: Moon is very small in comparison to earth.
If root mean square velocity of the gas molecules is less than escape velocity from that planet (or satellite) then atmosphere will remain attached with that planet and if vrms > vescape then there will be no atmosphere on the planet. This is the reason for no atmosphere at moon.
Assertion: Two different planets have same escape velocity.
Reason: Value of escape velocity is a universal constant.
As, escape velocity
so its value depends on mass of planet and radius of the planet. The two different planets have same escape velocity, when these quantities (mass and radius) are equal.
Assertion: Generally the path of a projectile from the earth is parabolic but it is elliptical for projectiles going to a very large height.
Reason: The path of a projectile is independent of the gravitational force of earth.
Upto ordinary heights, the change in the distance of a projectile from the centre of earth is negligible compared to the radius of earth. Hence the projectile moves under a nearly uniform gravitational force and the path is parabolic. But for the projectiles moving to a large height, the gravitational force decreases quite decreasing variable force, the path of the projectile becomes elliptical.
Assertion: Space rockets are usually launched in the equatorial line from west to east.
Reason: The acceleration due to gravity is minimum at the equator.
We know that earth revolves from west to east about its polar axis. Therefore, all the particles on the earth have velocity from west to east. This velocity is maximum in the equatorial line, as v=Rω, where R is the radius of earth and w is the angular velocity of revolution of earth about its polar axis. When a rocket is launched from west to east in equatorial plane, the maximum linear velocity is added to the launching velocity of the rocket, due to which launching becomes easier.
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