A cord is wound round the circumference of wheel of radius 'r'. The ax

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

Options:

A . √2ghI+mr

B . √2mghI+mr2

C . √2mghI+2mr2

D . √2gh

Answer: Option B
:
B
According to law of conservation of energy

m g h = \frac{1}{2} (I + m r^{2}) ω^{2} \Rightarrow ω = \sqrt{\frac{2 m g h}{I + m r^{2}}} .

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