A cord is wound round the circumference of a solid cylinder radius `R` and mass `M`. The axis of the cylinder is horizontal. A weight `mg` is attached to the end of the cord and falls from rest. After falling through a distance `h`.

Options

A. `(2mg)/(M+2m)`
B. `sqrt((2gh)/R^(2))`
C. `(sqrt(4mgh)/((M+2m)R^(2)))`
D. `sqrt((4mgh)/(M+2m))`

Answer

C

Explanation

`Mg-T=ma`……….i
`TR=(MR^(2))/2 .a/R`..ii
From energy conservation
`mgh=1/2 (MR^(2)omega^(2))/2+1/2momega^(2)R^(2)`
`sqrt((4mgh)/((M+2m)R^(2)))=omega`