Question

A ball of mass $m$ moving at a speed $v$ collides with another ball of mass 3m at rest. The lighter block comes to rest after collision. The coefficient of restitution is-

• A. $\frac{1}{2}$
• B. $\frac{2}{3}$
• C. $\frac{1}{4}$
• D. $None$ $of$ $these$.

Answer 1

Answer: (D)

$None$ $of$ $these$.

Coefficient of restitution$=e=$ Relative velocity of separation after collison(RVOS)/Relative velocity of approach before collision(RVOA);
velocity of mass $m$ before collision$=v$
velocity of mass $3m$ before collision$=0$
velocity of mass $m$ after collision$=0$
Let velocity of mass 3m after collision=v';
From conservation of momentum,

$mv+3m\times 0=m\times 0+3m{v}^{{}^{\prime }}$;

$\Rightarrow v^{\prime }=\frac{v}{3}$;

$e=\frac{RVOS}{RVOA}=\frac{\left(\frac{v}{3}\right)}{v}=\frac{1}{3}$