Question

A particle of mass m collides with another stationary particle of mass M. If the particle m stops just after the collision, the coefficient of restitution of collision is equal to:

• A. 1
• B. $\frac{m}{M}$
• C. $\frac{M - m}{M + m}$
• D. $\frac{m}{M + m}$.

Answer 1

Answer: (B)

$\frac{m}{M}$

Answer 2

The net horizontal force acting on the system (M+m) is zero. Therefore the momentum of the system just before and after the collision remains constant. Let M move with the velocity v'.

⇒ $m\overrightarrow{v} + 0 = m(0) + M\overrightarrow{v}$'

⇒ $\frac{v^{'}}{v} = ⥄ \frac{m}{M}$ …(1)

Newton’s experimental formula e = –$\frac{\left( v^{'} - 0 \right)}{0 - v}$

⇒ e = $\frac{v^{'}}{v}$ …(2)

Equating (1) and (2), we find e = (m/M).

Hence, (2) is correct choice.