The upper half of an inclined plane of inclination `theta` is perfectly smooth while lower half is rough . A block starting from rest at the top of the plane will again comes to rest at the bottom , if the coefficient of friction between the block and lower hald of the plane 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

The block may be stationary , when

`mgsintheta .L = mu mg cos theta L/2`
`rArr mu=(mgsintheta .L)/(mgcosthetaL/2) = 2(sintheta)/(costheta) = 2 tan theta`
`mu = 2 tan theta`