Solve the following :

Question:

A kid of mass $M$ stands at the edge of a platform of radius $R$ which can be freely rotated about its axis. The moment of inertia of the platform is $\mathrm{I}$. The system is at rest when a friend throws a ball of mass $m$ and the kid catches it. If the velocity of the ball is $v$ horizontally along the tangent to the edge of the platform when it was caught by the kid, find the angular speed of the platform after the event.

Solution:

Considering ball, boy and platform as system $L_{i}=L_{f}$

$\mathrm{mvR}=\left[1+(\mathrm{M}+\mathrm{m})^{R^{2}}\right] \omega$

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

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