A ball is dropped from a height of 10 m.

The potential energy decreases and the kinetic energy increases during the fall.

Its potential energy increases and kinetic energy decreases during the falls.

The potential energy is zero and kinetic energy is maximum while it is falling.

Its potential energy is equal to the kinetic energy during the fall.

A car is accelerated on a leveled road and attains a velocity 4 times of its initial velocity. In this process, the kinetic energy of the car

Becomes 16 times to that of the initial

Becomes twice to that of the initial

Becomes four times to that of the initial

The dimensional formula of Rotational Kinetic Energy is given by,

M¹ L² T^-2

Where,

Rotational Kinetic Energy (R.K_e) = 2^-1 × [Moment of Inertia] × [Angular velocity]². . . . (1)

Since, the moment of inertia (MOI) = Mass × (Radius of Gyration)²

∴ The dimensions of MOI = M¹ L²T⁰ . . . . . (2)

And, angular velocity = Δθ × t^-1

∴ the dimensional formula of angular velocity = [M⁰L⁰T^-1] . . . .(3)

On substituting equation (2) and (3) in equation (1) we get,

Rotational Kinetic Energy = 2^-1 × [Moment of Inertia] × [Angular velocity]²

Or, R.K_e = [M¹ L²T⁰] × M⁰L⁰T^-1]²= [M¹ L² T^-2].

Therefore, rotational kinetic energy is dimensionally represented as [M¹ L² T^-2].

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