Assertion : If the momentum of a body increases by 50%, its kinetic energy increases by 125%.
Reason : Momentum is proportional to velocity and kinetic energy is proportional to the square of the velocity.

Options

A. If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are true but Reason is not correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If both Assertion and Reason are false.

Answer

A

Explanation

`p prop v` and kinetic energy `KE prop v^2`
Increase in p by 50% means that v becomes `3/2` times, which increases the kinetic energy by `9/4` times. Therefore, increase in E is given by
`DeltaE = ((9//4)E - E)/(E) xx 100 = 125%`