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

Let `W_(g)` and `W_(f)` be the work done by gravity and frictional force . Using work energy theorem,
`W_(g) + W_(f) = Delta k`
mg (2 d sin `phi`) - ( `mu` mg cos `phi`) d = 0
`v = 2 tan phi`