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 is correct but R is not correct.

A is not correct but R is correct.

Both A and R are correct but R is NOT the correct explanation of A.

Center of Mass PYQ — JEE Main 2021 · 26 Feb · Shift 1 · Q59 with Solution

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Correct answer: C

For a head-on elastic collision where mass $M$ with initial speed $u$ collides with mass $m$ initially at rest, the final speed of body $Q$ is

$v_Q = \frac{2M}{M+m}\,u$

This result is obtained by using both:

Given $m \ll M$ ,

$M+m \approx M$

So,

$v_Q = \frac{2M}{M+m}u \approx \frac{2M}{M}u = 2u$

More precisely,

$v_Q = \frac{2M}{M+m}u < 2u$

but as $m/M \to 0$ , it approaches the maximum possible value $2u$ .

Hence the statement in Assertion A is taken as correct.

Reason R says: during elastic collision, both momentum and kinetic energy are conserved.

This is a standard fact for elastic collisions, so R is correct.

Yes. The expression

$v_Q = \frac{2M}{M+m}u$

is derived from conservation of momentum and kinetic energy. Then using $m \ll M$ , we get

$v_Q \approx 2u$

Therefore, R is the correct explanation of A.

The correct option is:

$\boxed{\text{C}}$

Both A and R are correct and R is the correct explanation of A.