A cord is wound round the circumference of wheel of radius `r`. The axis of the wheel is horizontal and fixed 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. `((2gh)/(l+mr))^(1//2)`
B. `((2mgh)/(l+mr^(2)))^(1//2)`
C. `((2mgh)/(l+2m))^(1//2)`
D. `(2gh)^(1//2)`

Answer

B

Explanation

By conservation of energy,
`mgh=(1)/(2)l omega^(2)+(1)/(2)mv^(2)`
`=(1)/(2)l omega^(2)+(1)/(2)mr^(2)omega^(2)=(omega^(2))/(2)[l+mr^(2)]`
`omega=[(2mgh)/(l+mr^(2))]^(1//2)`