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Question

A circular disc of radius R and mass m is hinged at the centre about horizontal axis. A particle of same mass is attached at the top of the disc. Now the system is released. Calculate the angular velocity of the disc when the particle reaches bottom.

A
8g3R
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B
7g3R
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C
2gR
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D
5g3R
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Solution

The correct option is A 8g3R
Let ω be angular velocitywhen mass reaches the bottom.
Now from conservation of angular momentum,

mg(2R)+0=12Iω2
2mgR=12(mR22+mR2)ω2
ω=8g3R

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