A solid cylinder of mass `m` is kept in balance on a fixed incline of angle `alpha=37^@` with the help of a thread fastened to its jacket. The cylinder does not slip.

The values of minimum coefficient of static friction between cylinder and incline in the case when `F` is minimum.

Options

A. `3/4`
B. `3/8`
C. `3/16`
D. none of these

Answer

B

Explanation

`F+f=mg sinalpha`
`implies f+f=mgsinalpha [:'F=]`
`implies f=(mgsinalpha)/2`
`f_(l)=muN=mumgcosalpha`

For no slipping `f_(e)gef`
`implies mumgcosalphagemg((sinalpha)/(2))`
`implies muge(tanalpha)/2=(3//4)/2=3/8`