A body of mass "m" having an initial velocity "v" makes head on elastic collision with a stationary body of mass "M". After the collision, the body of mass "m" comes to rest and only the body having mass "M" moves. This will happen only when

Explanation

In a perfectly elastic head-on collision, both momentum and kinetic energy are conserved. For the body of mass m to come to rest after the collision, its entire momentum must be transferred to the stationary body of mass M. This complete transfer occurs only when m equals M. Under this condition, the velocity of m is fully imparted to M, causing M to move with m's initial velocity and m to stop. For other scenarios: Option A: When m >> M, m's momentum is too large for M to absorb entirely, so both bodies continue moving.Option C: If m << M, m will stop, but M won't move with the full velocity of m, so both will move.Option D: With m = M/2, the transfer of momentum is incomplete, leading to both bodies moving post-collision.