The force required to just move a body up the inclined plane is double the force required to just prevent the body from sliding down the plane. The coefficient of friction is `mu`. If `theta` is the angle of inclination of the plane than `tan theta` is equal to

Options

A. `tan^(-1)(mu)`
B. `tan^(-1)(mu//2)`
C. `tan^(-1)(2mu)`
D. `tan^(-1)(3mu)`

Answer

D

Explanation

`F_(1)=mg sin theta+ mu mg cos theta`
`F_(1)=mg sin theta-mu mg cos theta`
`F_(1)=2F_(2)`
`therefore tan theta+mu=2 (tan theta-mu)`
`3mu=tan theta`
`theta=tan^(-1)(3mu)`