Question

An inclined plane is inclined at an angle $\theta$ with the horizontal. A body of mass $m$ rests on it, if the coefficient of friction is $\mu$, then the minimum force that has to be applied to the inclined plane to make the body just most up the inclined plane is-

• A. $\mu mg\cos \theta$
• B. $mg\sin \theta$
• C. $\mu mg\cos \theta -mg\sin \theta$
• D. $\mu mg\cos \theta +mg\sin \theta$

Answer 1

The correct option is C $\mu mg\cos \theta -mg\sin \theta$

As it is asked for the minimum force required to push the body up the incline plane. it must be equal to the net maximum force acting along the plane of incline.

So from the free body diagram, net force along the incline surface is $\mu mgcos\theta -mgsin\theta$

So $F >= $\mu mgcos\theta -mgsin\theta$$

$\therefore F_{min}=$$\mu mgcos\theta -mgsin\theta$