The minimum force required to move a body up on an inclined plane is three times the minimum force required to prevent it from sliding down the plane.If the coefficient of friction between the body and the inclined plane is `1/(2sqrt3)` the angle of the inclined plane is

Options

A. `60^@`
B. `45^@`
C. `30^@`
D. `15^@`

Answer

C

Explanation

Minimum force required to move a body up a rough inclined plane
`F_1 = mg (sin theta + mu cos theta)`
Minimum force required to prevent the body from sliding down the rough inclined plane.
`F_2 = mu mg cos theta`
According to question,
`F_1 = 3 F_2`
`therefore mg(sin theta - mu cos theta) = 3 (mu cos theta)`
`sin theta + mu cos theta = 3 mu cos theta`
`sin theta = 2 mu cos theta`
`2 xx 1/(2sqrt(3)) = 1/(sqrt3)`
`= tan 30^@`
`theta = 30^@`