Given below are two statements: one is labelled as Assertion (A)...

Evaluate Assertion (A):
The final velocity of a moving body of mass $m_1$ colliding elastically with a stationary target of mass $m_2$ is $v_1 = \dfrac{m_1 - m_2}{m_1 + m_2}u_1$.
The body only rebounds (i.e., $v_1$ is negative)$if m_1 < m_2$. If $m_1 > m_2$, it continues moving in the same direction. Therefore, it does not always rebound when the masses are different. Assertion (A) is false.

Evaluate Reason (R):
The fraction of kinetic energy transferred to a stationary target is $f = \dfrac{4m_1 m_2}{(m_1 + m_2)^2}$.
For a target of mass $2m$: $f = \dfrac{4(m)(2m)}{(m + 2m)^2} = \dfrac{8m^2}{9m^2} = \dfrac{8}{9}$.
For a target of mass $m/2$: $f = \dfrac{4(m)(m/2)}{(m + m/2)^2} = \dfrac{2m^2}{(1.5m)^2} = \dfrac{2}{2.25} = \dfrac{8}{9}$.
The fraction transferred is identical in both cases. Reason (R) is true.

Thus, (A) is false but (R) is true.

Answer: (A) is false but (R) is true