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