Question

Assertion (A): If momentum of a body increases by 50%, its kinetic energy will increase by 125%.

Reason (R): Kinetic energy is proportional to the square of velocity.

Options

• both A and R are true and R is the correct explanation of A.

• both A and R are true and R is not the correct explanation of A.

• assertion is false but reason is true.

• assertion is true but reason is false.

Answer 1

Both A and R are true and R is the correct explanation of A.

Explanationn:

If p increases by 50%, p' = 1.5p and \[ K' = \frac{(1.5p)^{2}}{2m} = 2.25K \], so the increase is 125%. The reason correctly explains this because kinetic energy is proportional to the square of velocity (and momentum is proportional to velocity).