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. `mu=(1)/(tan theta)`
B. `mu=(2)/(tan theta)`
C. `mu = 2tan theta`
D. `mu =tan theta`

Answer

c

Explanation

For the upper half of inclined plane
`upsilon^(2) = 2 a_(1)s` when `a_(1) = g sin theta`
For the lower half of inclined plane
`0 = upsilon^(2) - 2 a_(2)s` where `a_(2) = mu g cos theta - g sin theta`
From these two equations `a_(1) = a_(2)`
`g sin theta = mu g cos theta - g sin theta`
`2 g sin theta = mu g cos theta`
`2 tan theta = mu` .