Question

Given below are two statements : one is labelled as Assertion $A$ and the other is labelled as Reason $R$.

Assertion $A$: Body $P$ having mass $M$ moving with speed $u$ has head-on collision elastically with another body $Q$ having mass $m$ initially at rest. If $m<<M$, body $Q$ will have a maximum speed equal to $2u$ after collision.

Reason $R$ : During elastic collision, the momentum and kinetic energy are both conserved.

In the light of the above statements, choose the most appropriate answer from the options given below:

• A. $A$ is correct but R is not correct.
• B. Both $A$ and $R$ are correct but $R$ is NOT the correct explanation of $A$.
• C. $A$ is not correct but $R$ is correct.
• D. Both $A$ and $R$ are correct and $R$ is the correct explanation of $A$.

Answer 1

The correct option is D Both $A$ and $R$ are correct and $R$ is the correct explanation of $A$.

$m<<M$

$e=\frac{v_2-v_1}{u_1-u_2}$

[ Newton's Law of Restitution ]

For elastatic collision, $e=1$

$1=\frac{v_2-u}{u-0}$

$u=v_2-u$

$v_2=2u$

In elastic collision kinetic energy & momentum are conserved.

Hence, option (d) is the correct answer.