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 come to rest at the bottom, if the coefficient of friction between the block and lower half of the plane 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`