Question

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

• A. $\sqrt{\frac{2gh}{I + mr}}$
• B. $\sqrt{\frac{2mgh}{I + mr^{2}}}$
• C. $\sqrt{\frac{2mgh}{I + 2mr^{2}}}$
• D. $\sqrt{2gh}$

Answer 1

Answer: (B)

$\sqrt{\frac{2mgh}{I + mr^{2}}}$

Answer 2

According to law of conservation of energy

$mgh = \frac{1}{2}(I + mr^{2})\omega^{2}$ $\Rightarrow$ $\omega = \sqrt{\frac{2mgh}{I + mr^{2}}}$.