In the situation shown, the force required to just move a body up an inclined plane is double the force required to just prevent the body from sliding down the plane. The coefficient of friction between the block and plane is `mu`. The angle of inclination of the plane from horizontal is given by :

Options

A. tan `theta = mu`
B. tan `theta = 2 mu`
C. tan `theta = 0.5 mu`
D. tan `theta = 3 mu`

Answer

D

Explanation

Force required to just move the body up the inclined plane is `F_(1) = mg sin theta + mu m g cos theta`
Force required to just prevent sliding is `F_(2) = m g sin theta = mu g cos theta`
Given `F_(1) = 2F_(1) implies (m g sin theta + mu m g cos theta) = 2 (m g sin theta - mu m g cos theta)`
`implies tan theta + mu = 2 (tan theta - mu) implies tan theta = 3 mu`