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

Gain of kinetic energy = loss of KE due to firiction in lower half.

`mg sin theta S=mu mg cos theta S//2`
`mu=2 tan theta `