Question

A block of mass m testing on a inclined plane as shown in fig. The inclination of the plane to the horizontal is gradually increasing. It is found that when the angle of inclination is $\theta$, the block just begin to slide down the plane. What the minimum force F applied parallel to the plane that would just make the block move up to the plane.

• A. $2mgsin\theta$
• B. $mgsin\theta$
• C. $mgcos\theta$
• D. $2mgcos\theta$

Answer 1

The correct option is A $2mgsin\theta$

The component of weight $mg$ of the block along the inclined plane $=mg\sin \theta$.

The minimum frictional force to be overcome is also $=mg\sin \theta$

To make the block just move up the plane the minimum force applied must overcome the component $mg\sin \theta$ of gravitational force as well as the frictional force $mg\sin \theta =2mg\sin \theta$