UPSC NDA 2 2019 General Ability Solved Paper

Concept:Momentum is a vector quantity; it depends on direction. In a perfectly elastic collision with the ground (no energy loss), only the direction of velocity reverses, while speed and kinetic energy remain unchanged.Explanation:Let the ball have mass $m$ and speed $v$ just before hitting the ground.Before the bounce, the velocity is downward; momentum is $p_i = m v$ (downward).After the bounce, the velocity is upward with same speed $v$; momentum is $p_f = -m v$ (upward).The magnitude of momentum remains $mv$, but its direction reverses completely.Since momentum is a vector, this reversal means a sudden change: $\Delta p = p_f - p_i = -m v - (m v) = -2 m v$.Speed (magnitude of velocity) stays $v$ – no change.Kinetic energy $=\frac12 m v^2$ depends only on $v$ and $m$; with no energy loss, it does not change.Potential energy relative to ground is $mgh$; at the instant of bounce $h=0$, so potential energy is zero both before and after – no sudden change.Thus, only momentum changes suddenly during the bounce.Answer:B. Its momentum