The force required just to move a body up an inclined plane is double the force required just to prevent the body sliding down. If the coefficient of friction is `0.25` , the angle of inclination of the plane is

Options

A. `30^(@)`
B. `45^(@)`
C. `tan^(-1) ((1)/(4))`
D. `tan^(-1)((3)/(4))`

Answer

D

Explanation

`F_(1) = mg sin theta + f_(max)`
`= mg sin theta + mu mg cos theta`
`mg sin theta = F_(2) + f_(max)`
`F_(1) = 2 F_(2)`
`mg sin theta + mu mg cos theta = 2(mg sin theta - mu mg cos theta)`
`3 mu cos theta = sin theta`
`tan theta = 3mu = (3)/(4) rArr theta = tan^(-1) ((3)/(4))`

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