Question

Assertion :Two bodies of different masses have same momentum. Their kinetic energies are in the inverse ratio of their masses. Reason: K.E. = $0.5m{v}^2$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

We can express kinetic energy of a particle in terms of its momentum.

Since v = $\frac{p}{m}$ and the kinetic energy K = $\frac{1}{2}$mv${}^2$ so,

K = $\frac{1}{2}$m($\frac{p}{m})$${}^2$ = $\frac{p^2}{2m}$.

So if a massive particle and a light particle have a same momentum, the light will have a lot more kinetic energy.If a light particle and a heavy one have a same velocity, the heavy one has more kinetic energy. Thus the two bodies will have same momentum and its kinetic energies will be in inverse ratio of their masses. Hence both assertion and reason are correct and reason is the correct explanation for assertion.