Question

A particle of mass $m$ and speed $v$ collides elastically with the end of a uniform thin rod of mass $M$ as shown in the figure. After the collision, $m$ is stationary. Calculate the ratio of masses $(\frac{M}{m})$.

• A. $6$
• B. $5$
• C. $2$
• D. $3$

Answer 1

Answer: (D)

$3$

Applying conservation of momentum: $mv=M{v}^{\prime }$ ......(1) where $v^{\prime }$ is the velocity of COM of the rod after collision.
Applying conservation of angular momentum:

$mv\frac{l}{2}=I\omega =\frac{M{l}^2}{12}\omega =\frac{M{l}^2}{12}\times \left(\frac{v^{\prime }}{\frac{l}{2}}\right)=\frac{Ml{v}^{\prime }}{6}=\frac{Ml}{6}$

$\Rightarrow \frac{m}{M}=\frac{2}{6}=\frac{1}{3}$

$\therefore \frac{M}{m}=3$