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Q.

A string is wrapped around a wheel of radius ‘r’. The axis of the wheel is horizontal and its M.I. about the axis is I. Weight ‘mg’ is tied to free end of the string which is released to fall down from rest position. The angular velocity of the wheel after it has fallen through distance ‘h’ will be

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a

(2ghI+mr2)12

b

(2mghI+mr2)12

c

2mghI+2mr2

d

2gh

answer is B.

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Detailed Solution

mgh=12m ϑ2+12Iω2                 = 12mr2ω2+12Iω2                 mgh=12ω2(mr2+I)                 ω=2mghI+mr2
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A string is wrapped around a wheel of radius ‘r’. The axis of the wheel is horizontal and its M.I. about the axis is I. Weight ‘mg’ is tied to free end of the string which is released to fall down from rest position. The angular velocity of the wheel after it has fallen through distance ‘h’ will be