Question

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

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

Answer 1

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

Mass of the boy$=M$

Radius$=R$

Moment of Inertia$=I$

Mass of ball$=m$

Velocity$=\upsilon$

The angular momentum is conserved for a system.

So,

$m\upsilon R=[I\omega +\omega (M+m)R^2]$

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