Given below are two statements :

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 $\$ m<$ 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. (1) $\mathrm{A}$ is correct but $\mathrm{R}$ is not correct.

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

  3. (3) $\mathrm{A}$ is not correct but $\mathrm{R}$ is correct.

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

Correct Option: 4,

Solution:

(4)

$m<

$e=\frac{V_{2}-V_{1}}{u_{1}-u_{2}}$

For elastic collision $\rightarrow \mathrm{e}=1$

$1=\frac{v_{2}-u}{u-0}$

$\mathrm{u}=\mathrm{v}_{2}-\mathrm{u}$

$v_{2}=2 u$

In elastic collision kinetic energy \& momentum are conserved.

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