Question

Ball $1$ Collides head-on with another identical ball $2$ at rest. The velocity of ball $2$ after collision becomes two times to that of ball $1$ after a collision. The coefficient of restitution between the two balls is

• A. $e=1/3$
• B. $e=1/2$
• C. $e=1/4$
• D. $e=2/3$

Answer 1

The correct option is A $e=1/3$

Both balls have mass 'm'.
Initially ball 1 moves with v.
After collision ball 1 moves with $v_2$
After collision ball 2 moves with $2v_2$
Momentum is conserved.
i.e.
$mv=m{v}_2+2m{v}_2=3m{v}_2$
i.e.
$v_2=\frac{v}{3}$
Velocity of approach $=v-0=v$
Velocity of separation $=\frac{2}{3}v-\frac{1}{3}v=\frac{1}{3}v$
Coefficient of restitution is velocity of approach by velocity of separation.
$e=\frac{v/3}{v}=\frac{1}{3}$