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Question

As shown in the figure, a bob of mass m is tied by a massless string whose other end portion is wound on a fly wheel (disc) of radius r and mass m, when released from rest the bob starts falling vertically. When it has covered a distance of h, the angular speed of the wheel will be :



A

r34gh
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B

r32gh
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C

1r2gh3
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D
1r4gh3
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Solution

The correct option is D 1r4gh3

Applying energy conservation principle we get,
Loss in P.E. of bob = gain in total K.E. of wheel

mgh=12mv2+12Iω2

where,
(v=ωr) is the velocity of disc with which the disc is rotating,
I=12mr2 is the moment of inertia of disc about its centre.

Substituting the values,
mgh=12m[rω]2+12mr22ω2

gh=r2w2[12+14]

gh=34r2w2

ω2=4gh3r2

Thus, Angular speed of wheel , ω=1r4gh3

Hence, option (d) is the correct answer.

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