Question

A heavier body moving with certain velocity collides head on elastically with a lighter body at rest. Then

• A. smaller body continues to be in the same state of rest
• B. smaller body starts to move in the same direction with same velocity as that of bigger body
• C. the smaller body starts to move with twice the velocity of the bigger body in the same direction
• D. the bigger body comes to rest

Answer 1

Answer: (C)

the smaller body starts to move with twice the velocity of the bigger body in the same direction

Let the velocity of bigger ball be $v$.
Mass be $M>>$ mass of small ball($m$)
After collision, let the velocities be $v_1$ and $v_2$ respectively.
Hence, conserving momentum:
$Mv=M{v}_1+m{v}_2$
And for elastic collision:
$v=v_2-v_1$
=> $v_1=v_2-v$
Replacing this in momentum equation:
$Mv=M{v}_2-Mv+m{v}_2$
=> $v_2=2v\left(M/\right(M+m\left)\right)$ which approximates to $2v$, the limit $M>>m$