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

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

Options

A $\dfrac{2mgh}{I + m{r}^{2}}$
B $\dfrac{2mgh}{I + 2m{r}^{2}}$
C $2gh$
D $\dfrac{2gh}{I + m{r}^{2}}$

Correct answer

A. $\dfrac{2mgh}{I + m{r}^{2}}$

Step-by-step solution

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

$mgh = \dfrac{1}{2}I{\omega}^{2} + \dfrac{1}{2}m{v}^{2}$

$v = \omegar$

$mgh = \dfrac{1}{2}I{\omega}^{2} + \dfrac{1}{2}m{\omega}^{2}{r}^{2}$

$\dfrac{2mgh}{\left(I + m{r}^{2}\right)} = {\omega}^{2}$

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