The upper half of an inclined plane with inclination `phi` is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by

Options

A. `mu=(1)/( tan theta)`
B. `mu=(2)/( tan theta)`
C. `mu= 2 tan theta`
D. `mu= tan theta`

Answer

C

Explanation

( c) The block may be stationary, when

`mg sin theta.L=mu mg cos theta (L)/(2)`
`implies mu=(mg sin theta. L)/(mg cos theta(L)/(2))=2(sin theta)/(cos theta)=2 tan theta`
` mu =2 tan theta`