A cord is wound round the circumference of wheel of radius r , The axis of the wheel is horizontal and the…

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
  1. 2mghI+mr2
  2. 2mghI+2mr2
  3. 2gh
  4. 2ghI+mr2

Solution

mgh=12Iω2+12mv2

v=ωr

mgh=12Iω2+12 mω2r2

2mghI+mr2=ω2

Asked in: JEE Main 2021 (26 Feb Shift 2)

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