The minimum force required to move a body up 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 `(1)/(2sqrt3)`,is the angle of the inclined plane is

Options

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

Answer

(c)

Explanation

`mu= (1)/(2sqrt3)`,
`F_(up)=3F_(down)(given)`
`Rightarrow mg(sin theta+mucostheta)=3[mu mg cos theta]`
`Rightarrow sin theta+mucostheta=3mu mg cos theta`
`Rightarrow sin theta=3mucostheta-3mu`
`Rightarrow sin theta=2mucostheta`
`tantheta=2mu=2(1)/(2sqrt3)`
` therefore theta=30^(@)`