A kid of mass M stands at the edge of a platform of radius r which can freely rotate about its axis. The moment of inertia of platform is 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.

Question

$$\begin {array} {1 1} (a)\;\frac{2mvr}{I+(M+m)r^2} & \quad (b)\;\frac{mvr}{I+(M+m)r^2} \\ (c)\;\frac{Mvr}{I+(M+m)^2} & \quad  (d)\;\frac{mvr}{I+Mr^2} \end {array}$$