The upper half of an inclined plane with an angle of inclination 4, is smooth while the lower half is rough. A body starting from rest at the top of the inclined plane comes to rest at the bottom of the inclined plane. Then the coefficient of friction for the lower half is

Options

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

Answer

A

Explanation

For upper half
`U=0,S=l//2`
`V^(2)=U^(2) + 2as``V^(2) = 0 + 2(g sin phi) l//2`
For lower half
`V= 0 and a = g (sin (phi) - mucos phi)`
`0 = U^(2) + 2g (sin (phi) - mu cos phi) l//2`
`imples U^(2) = - g (sin phi – mu cos phi) l`
`implies g I sin phi = - g I (sin phi - mu cos phi)`
`implies 2 sin phi = mu cos phi`
`therefore mu = 2 tan phi`