A uniform cylinder of mass `m` lies on a fixed plane inclined at a angle `theta` with the horizontal. A light string is tied to the cylinder at the rightmost point, and a mass `m` hangs from the string as shown. Assume that the coefficient of friction between the cylinder and the incline plane is sufficiently large to prevent slipping. for the cylinder to remain static the value of `m` is

Options

A. `(Msintheta)/(1-sintheta)`
B. `(Mcostheta)/(1+sintheta)`
C. `(Msintheta)/(1+sintheta)`
D. `(Mcostheta)/(1-costheta)`

Answer

A

Explanation

`T=mg`

`f=Mgsintheta+Tsintheta=Mgsintheta+mgsintheta`
Balancing torque about C
`Tr=fr`
`implies mg=Mg sintheta+mgsintheta`
`implies m=(Msintheta)/(1-sintheta)`