The upper half of an inclined plane of inclination `theta` is perfectly smooth while the lower half rough. A block starting from rest at the top of the plane will again come to rest at the bottom if the coefficient of friction between the block and the lower half of plane in given by

Options

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

Answer

A

Explanation

(a) `v^(2)=2a_(1)s(a_(1)=g sin theta)`
`0=v^(2)-2a_(2)s(a^(2)=mu g cos theta-g sin theta)`
From these two equations we see that `a_(1)=a_(2)`
`implies" " g sin theta=mu g cos theta-g sin theta implies 2 tan theta =mu`