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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
mvRI+mR2
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B
mvR1+MR2
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C
mVR(M+m)R2
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D
mvR1+(M+m)R2
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Solution

The correct option is D mvR1+(M+m)R2
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)R2]ω
where ω 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]

ω=mvRI+(M+m)R2

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