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`.

If the mass starts from rest and falls a distance `h`, then its speed at that instant is:

Options

A. proportional to `R`
B. proportional to `1/R`
C. propotional to `1/R^(2)`
D. independent of `R`

Answer

D

Explanation

`mgh=1/2(MR^(2))/2.(v^(2))/(R^(2))+1/2mv^(2)`
`4mgh=Mv^(2)=2mv^(2)implies v=sqrt((4mgh)/(M+2m))`
which is independent of `R`
`i.e., vpropR^(2)`