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A uniform cylinder of mass M lies on a f...

A uniform cylinder of mass `M` lies on a fixed plane inclined at an angle `theta` with horizontal. A light string is tied to the cylinder at the right most 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 the remain static, the value of `m` is

A

`(Msintheta)/(1-sintheta)`

B

`(Mcostheta)/(1+sintheta)`

C

`(Msintheta)/(1+sintheta)`

D

`(Mcostheta)/(1-costheta)`

Text Solution

Verified by Experts

The correct Answer is:
A
`T=mg`

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