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Question

A block of mass m is suspended from a pulley in the form of a circular disc of mass m and radius R. The system is released from rest. Find the angular velocity of the disc when the block has dropped by height h. [Assume there is no slipping between string & pulley]


A
1R4gh3
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B
1R2gh3
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C
R2gh3
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D
R4gh3
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Solution

The correct option is A 1R4gh3
By conservation of mechanical energy:-
TEi=TEf
Initial P.E of block = Final P.E of block + Final K.E of block and pulley
Take final P.E of block as zero (reference point). Let the final velocity of block be v and final angular velocity of disc be ω.
Then, mgh=12mv2+12Iω2
As we know,
v=ωR (for no slipping condition)
and, Idisc=mR22

mgh=12mω2R2+12mR22ω2
mgh=34mω2R2
ω=4gh3R2=1R4gh3

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