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. `sqrt((2gh)/(I+mr))`
B. `[(2mgh)/(I+mr^(2))]^(1//2)`
C. `[(2mgh)/(I+2mr^(2))]^(1//2)`
D. sqrt(2gh)

Explanation

Loss in potential energy `=` gain in `K.E.`
`mgh=(1)/(2)mv^(2)+(1)/(2)Iomega^(2)=(1)/(2)m(romega)^(2)+(1)/(2)Iomega^(2)`
`omega=sqrt((2mgh)/(I+mr^(2)))`