A massless rope is wrapped several times on a disc of mass M and radius R. The other end is tied to a mass m which at the beginning is at a height of h above ground as shown in the figure. When released the velocity of the mass as it touches the ground is

Options

A. `sqrt((4mgh)/(2m+M))`
B. `sqrt(2gh)`
C. `sqrt((4mgh)/(3M))`
D. `sqrt((4mgh)/(M+m))`

Answer

1

Explanation

`tau=Ialpha" " rArr TR=1/2 MR^(2)(a/R)`
`rArr T=1/2 Ma` and `mg-T=ma`
`mg =ma+1/2 Ma `or `a=(2mg)/(M+2m)`
Velocity after a fall of height h is
`v^(2)=2ah`
`v=sqrt(2ah)=sqrt((4mgh)/(M+2m))`