A cord is wrapped on a pulley (disk) of mass `M` and radius `R` as shown in Fig. To one end of the cord, a block of mass `M` is connected us shown and to other end in (a) a force of `2 Mg` and in (b) a block of mass `2M`. Let angular acceleration of the disk in `A` and `B` is `alpha_(A)` and `alpha_(B)`, respectively, then (cord is not slipping on the pulley).

Options

A. `f_(a)=f_(b)`
B. `f_(a)=f_(b)//2`
C. `f_(a)=f_(b)//3`
D. `f_(a)=2f_(b)`

Answer

C

Explanation

`f_(a)=((2m-m)/(2m+m))g=g/3`
`f_(b)=(2mg-mg)/m=g`
So, `f_(a)=f_(b)//3`