Question

A boy of mass $M$ stands at the edge of a circular platform of radius $R$ capable of rotating freely about its axis. The moment of inertia of the platform about the axis is $I$. The system is at rest. A friend of the boy throws a ball of mass $m$ with a velocity $v$ horizontally. The boy on the platform catches it when it passes tangentially to the platform. Find the angular velocity of the system after the boy catches the ball.

• A. $\frac{mvR}{I+m{R}^2}$
• B. $\frac{mvR}{1+M{R}^2}$
• C. $\frac{mVR}{(M+m)R^2}$
• D. $\frac{mvR}{1+(M+m)R^2}$

Answer 1

The correct option is D $\frac{mvR}{1+(M+m)R^2}$

Considering the ball, boy and disc as a system.
Here, net external torque is zero.
So, applying conservation of angular momentum,
$mvR=[I+(M+m\left)R^2\right]\omega$
where $\omega$ is the final angular velocity of system & $I$ is moment of inertia of the platform about its axis.

[since the boy is at the edge of the platform when he catches the ball, angular momentum of the ball just before catching $=mvR$]

$\Rightarrow \omega =\frac{mvR}{I+(M+m)R^2}$