Concept:

• the dimensional formula is defined as the expression of the physical quantity in terms of mass, length, and time.
• The turning momentum of particle about the axis of rotation is called the angular momentum of the particle. Mathematically angular momentum can be written as
• Either Angular momentum is the rotational analog of linear momentum. The angular momentum of an object can also be connected to the angular velocity ω of the object via the moment of inertia I.

• ∴ L = I x ω = r x p

  Where, L = angular momentum, I = moment of inertia, ω = angular momentum,

  r = distance and p = linear momentum = (m×v) .

Explanation:

Now,

Dimensional formula of (r) = [L],

Dimensional formula of (p) = [MLT^-1],

Therefore, the dimensional formula of L is

L = [L] × [MLT^-1]

∴ L = [ML²T^-1]

∴ Dimensional formula of angular momentum L is [ML²T^-1].

This are some of the useful dimensions of basic physical quantity, Here M, L, T & I represents mass, Length, Time and Current respectively.

The maximum velocity of the vehicle by which it can be driven before overturning is given by v = (gra/h)^1/2

g = acceleration due to gravity

r = radius of the curved path

2a = length of axle

h = height of the centre of mass of vehicle above ground

Thus, bigger the vehicle, easily it will overturn due to the inverse relation

Larger the radius of the path, easily it can move without overturn

Concept:

3 equations of motion govern the position of any particle:

v = u + at

s = ut + 1/2at²

v² = u² + 2as

Application of Concept:

When the body is thrown upwards, at the top most point its final velocity becomes zero

Using third equation of motion

v² =u² + 2as

v = 0

a = -g

− u² = 2(−g)s

s = u²/2g

The moment of inertia of a rectangle of width b and height d, about each of its centroidal axis, is:

From the conservation of momentum

m_au_a + m_bu_b = m_av_a + m_bv_b

Considering the bow and arrow as one mass system

m_a = 10-gm

u_a = 300 m/s

m_b = 150-gm

u_b = ?

10 (300) + 150 (u_b) = 0

Recoil Velocity = 20 m/s

The negative sign shows that the bow moves in the opposite direction to the arrow.

Common Mistake:

A common mistake that a student can make is assuming the answer as  - 20 m/s

It should be noted that the term "recoil velocity" has been used in the question that will take care of the direction and hence the negative sign. 

In case of small drops of a liquid, the gravitational potential energy is negligible in comparison to the potential energy due to surface tension. Consequently, to keep the drop-in equilibrium, the liquid drop’s surface tends to contract so that its surface area will be the least for a sphere and the drops will be spherical.

So, small drops of liquid are spherical because surface tension predominates over that of gravity and bigger drops are oval.

• A Period is the smallest interval of time after which a periodic motion repeats itself. Its SI unit is second.
• Displacement is the change in the position of an object undergoing periodic motion.
• The maximum displacement of an object is called its amplitude.
• Frequency is the total number of periodic motions that can be executed by a body in 1 second.

Heat energy of an object is the overall energy of the molecules that arise due to the motion of the molecules.

According to Ohm’s Law, Power P = VI

⇒ I = P/V

⇒ I = 620/310

⇒ I = 2A