Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
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 $\mathrm{m}<<\mathrm{M}$, 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 :

1. $A$ is not correct but $R$ is correct.

2. Both $\mathrm{A}$ and $\mathrm{R}$ are correct but $\mathrm{R}$ is NOT the correct explanation of $\mathrm{A}$.

3. Both $\mathrm{A}$ and $\mathrm{R}$ are correct and $\mathrm{R}$ is the correct explanation of $A$.

4. $A$ is correct but $R$ is not correct.

Correct Option: , 3

Solution:

For $\mathrm{e}=1 \&$ second body at rest

$V_{2}=\frac{2 m_{1} u_{1}}{m_{1}+m_{2}}=\frac{2 u(M)}{M+m} \simeq 2 u$

Since $M \gg m$