Question

A uniform rod of length $l$ and mass $M$ rotating about a fixed vertical axis on a smooth horizontal table. It elastically strikes a particle placed at a distance $3m$ from its axis and stops. Mass of the particle is :

• A. $3M$
• B. $\frac{3M}{4}$
• C. $\frac{3M}{2}$
• D. $\frac{4M}{3}$

Answer 1

The correct option is B $\frac{3M}{4}$

Using the conservation of angular momentum we have
$I_1{\omega }_1+m{v}_{1}r=I_2{\omega }_2+m{v}_{2}r$
or
$\frac{M{l}^2}{12}\times \frac{v}{L/3}+0=0+\frac{L}{3}mv$
here v is the velocity of the particle and that of the impact point on the rod.
Solving we get
$m=\frac{3M}{4}$