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

Options

A. Statement I is True, Statement II is True, Statement II is a correct explanation for Statement I
B. Statement I is True, Statement II is True, Statement II is not a correct explanation for Statement I
C. Statement I is True, Statement II is False.
D. Statement I is False, Statement II is True.

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 +M V 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 Mu)/((M + m)) = (2u)/((1 + m/M))`
If `M gt gt m`, then v is maximum equal to 2u (since `m/M implies 0`)