Question

A particle of mass 'm' moving with velocity 'V', hits to a stationary disc of mass M and radius R and sticks to the disc on its rim. The angular velocity of the disc with which it starts to rotate about its centre is

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Here we consider both the particle and disc as a single system
$\therefore$ Torque due to internal forces do not change the angular momentum of the system.
$\therefore L_i=L_f$ where $L_i=mVR$ [w.r.t the centre of disc]
$L_f=I\omega +m{R}^2\omega$ [w.r.t the centre of disc]
$\therefore mVR=I\omega +m{R}^2\omega$
$\Rightarrow mVR=\frac{M{R}^2}{2}\omega +m{R}^2\omega$
$\Rightarrow \omega =\frac{V}{R}-\frac{M}{2m}$