Question

A particle of mass $m$ and velocity $v_0$ is fired at a solid cylinder of mass $M$ and radius $R$. The cylinder is initially at rest and is mounted on a fixed horizontal axle that runs through the centre of mass. The line of motion of the particle is perpendicular to the axle and at a distance $d$ (less than $R$) from the centre. If the particle sticks to the surface of the cylinder, then angular speed of the system just after the particle sticks is

• A. $\frac{2m{v}_{0}d}{R^2(M+2m)}$
• B. $\frac{2m{v}_{0}d}{R^2(M+m)}$
• C. $\frac{m{v}_{0}d}{R^2(M+2m)}$
• D. $\frac{2M{v}_{0}d}{R^2(M+2m)}$

Answer 1

The correct option is A $\frac{2m{v}_{0}d}{R^2(M+2m)}$

Let $\omega$ be angular velocity of system after collision
Conserving angular momentum about centre,

$m{v}_{0}d=(\frac{1}{2}M{R}^2+m{R}^2)\omega$
$\omega =\frac{2m{v}_{0}d}{R^2(M+2m)}$