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. `2 sin phi`
B. `2 cos phi `
C. `2 tan phi`
D. `tan phi`

Answer

C

Explanation

Work done on the object of mass m for complete displacement is equal to the work dne over the smooth surface and that over rough surface , that is shown in below :
`mgs sin phi = mg sin phi (s/2) + ( mu mg cos phi - mg sin phi) .s/2 `
`mgs sin phi = mu mgcos phi .(s/2)`
`mu = 2 tan phi`