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. $\sqrt{\frac{2mgh}{I+m{r}^2}}$
• C. $\sqrt{\frac{2mgh}{I+2m{r}^2}}$
• D. $\sqrt{2gh}$

Answer 1

The correct option is B $\sqrt{\frac{2mgh}{I+m{r}^2}}$

According to law of conservation of energy $mgh=\frac{1}{2}(I+m{r}^2){\omega }^2\Rightarrow \omega =\sqrt{\frac{2mgh}{I+m{r}^2}}.$