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Q.

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

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a

1r4gh3

b

1r2gh3

c

r32gh

d

r34gh

answer is A.

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Detailed Solution

Loss in potential energy is gain in translational bob and rotational disc kinetic energy.⇒mgh=12mv2+12lω2                     here,    v=ωr no slipping⇒mgh=12mω2r2+12mr22ω2    ⇒mgh=34mω2r2    ​⇒  ω=4gh3r2=1r4gh3
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