The upper half of an inclined plane with inclination 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 sinphi`
B. `2 cos phi`
C. `2 tan phi`
D. `tan phi`

Answer

c

Explanation

For first half of motion
, `upsilon^(2) = 2 (g sin phi)l`
...(a)
For second half of motion
`0= upsilon^(2) +2g (sin theta+mu cos phi)l...(b)`
Solving (a) and (b) we get
`mu = 2 tan phi`
Hence choice is (c).