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A cord is wound round the circumference of wheel of radius r. The axis of the wheel is horizontal and the moment of inertia about it is I. A weight mg is attached to the cord at the end. The weight falls from rest. After falling through a distance ‘h’, the square of angular velocity of wheel will be:

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a

2mghI+mr2

b

2gh

c

2mghI+2mr2

d

2ghI+mr2

answer is A.

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Detailed Solution

Decrease In P.E of block = Increase in K.E of wheel + block ⇒mgh=12mv2+12Iω2 where v=ωr⇒mgh=12mω2r2+12Iω2⇒ω2=2mghI+mr2

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A cord is wound round the circumference of wheel of radius r. The axis of the wheel is horizontal and the moment of inertia about it is I. A weight mg is attached to the cord at the end. The weight falls from rest. After falling through a distance ‘h’, the square of angular velocity of wheel will be: