A cord is wound round circumference of wheel of radius r . axis of wheel is horizontal and moment of

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6.System of Particles and Rotational Motion

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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

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} $

Solution

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}}}} $.

Standard 11

Physics

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