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. (a) `2 cos phi`
B. (b) `2 sin phi`
C. (c) `tan phi`
D. (d) `2 tan phi`

Answer

D

Explanation

According to work-energy theorem, `W=DeltaK=0`
(Since initial and final speeds are zero)
`:.` Work done by friction + Work done by gravity =0
i.e., `-(mu mg cos phi)l/2+mg l sin phi =0`
or `mu/2 cos phi = sin phi` or `mu=2 tan phi`