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Q)

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.

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

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A)
Initial angular momentum about axis $=mvr$.
Final angular momentum $=\bigg[ I+ (Mr^2+mr^2)\bigg ]w$
By angular momentum conservation $mvr= \bigg[I+ (M+m)r^2\bigg]w$
$w= \large\frac{mvr}{I+(M+m)r^2}$

 

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