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

Answer

a

Explanation

For first half acceleration `= g sin theta` Therefore, velocity after travelling ball distance

`v^(2) = 2(g sin theta)l`
For second half, acceleration
`= g(sin theta - mu_(k) cos theta)`
so `0^(2) = v^(2) = 2g (sin phi - mu_(k) cos phi)l`
Solving (i) and (ii) we get `mu_(k) = 2 tan theta`