A solid cylinder is rolling without slipping on a plane having inclination `theta` and the coefficient of static friction `mu_(s)`. The relation between `theta` and `mu_(s)` is

Options

A. `tanthetage3mu_(s)`
B. `tanthetagt3mu_(s)`
C. `tanthetale3mu_(s)`
D. `tan thetalt3mu_(s)`

Answer

C

Explanation

`a=(gsintheta)/((1+K^(2)//R^(2)))`
`a=(2)/(3)g sin theta["As"(K^(2))/(R^(2))=(1)/(2)]`
The torque
`tau=fR=I alpha`
implies `fR=(MR^(2))/(2)alpha`
Since, `R alpha=a implies f R=(MR)/(2) a`
implies `f=(Ma)/(2)`
`f=(M)/(2).(2)/(3)gsintheta`
implies `mu_(s)mg cos theta=(m)/(3)g sin thetaimplies mu_(s)=(tantheta)/(3)`
For rolling without slipping
`tan thetale3mu_(s)` .