Assertion : A body P of mass M moving with speed u collides head-on and elastically with a body Q of m initially at rest. If `m lt lt M`, body Q will have maximum speed equal to 2u after the collision.
Reason : In an elastic collision, the momentum and kinetic energy are both conserved.

Options

A. If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are true but Reason is not correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If both Assertion and Reason are false.

Answer

A

Explanation

If v and V are the velocity of Q and P after collision, then from conservation of momentum and KE, we have
`M u + m v + MV implies m(u - V) = m u " " .....(1)`
`1/2 M u^2 = 1/2 mv^2 + 1/2 MV^2 implies M(u - V) (u + V) = mv^2 " " ....(2)`
From eqns. (1), 2), we get `v = (2 M u)/((M + m)) = (2u)/((1 + m/M))`
If `M gt gt m`, then v is maximum equal to 2u (since `m/M implies 0`)