A particle of mass ' $\mathrm{m}$ ' collides with another stationary particle of mass ' $M$ '. Particle of…
A particle of mass ' $\mathrm{m}$ ' collides with another stationary particle of mass ' $M$ '. Particle of mass ' $m$ ' stops just after collision. The coefficient of restitution is
$\frac{M}{m}$
$\frac{\mathrm{m}+\mathrm{M}}{\mathrm{M}}$
$\frac{M-m}{M+m}$
$\frac{\mathrm{m}}{\mathrm{M}}$
Solution
Let $v$ be the velocity of mass $m$ and $v$ ' be the velocity of mass $M$ after collision.'
By law of conservation of momentum
$\begin{aligned}
& \mathrm{mv}=\mathrm{Mv} \\
& \therefore \frac{\mathrm{v}^{\prime}}{\mathrm{v}}=\frac{\mathrm{m}}{\mathrm{M}}
\end{aligned}$
Coefficient of restitutions,
$\mathrm{e}=\frac{\text { Re lative velocity after collision }}{\text { Relative velocity before collision }}=\frac{\mathrm{v}^{\prime}}{\mathrm{v}}=\frac{\mathrm{m}}{\mathrm{M}}$