Question

A body rests on a rough horizontal plane. A force is applied to the body directed towards the plane at an angle $\alpha$ with the vertical. The body can be moved along the plane

• A. only if $\alpha$ is greater than the angle of friction
• B. only if $\alpha$ is lesser than the angle of friction
• C. only if $\alpha$ is equal to the angle of friction
• D. for all values of $\alpha$

Answer 1

The correct option is A only if $\alpha$ is greater than the angle of friction

Consider a block placed on a rough horizontal plane. Now, the reaction force $\overrightarrow{R}$ is because it is equal and opposite to the weight $\overrightarrow{W}$ . If the force $\overrightarrow{F}$ is applied to the block towards the plane at an angle $\theta$, the resolved forces will act along vertical and horizontal direction.
The horizontal component of force $F\sin \theta$ have to overcome the frictional force so that the block just begins to slide. Frictional force is equal to limiting friction $F_{limiting}$, when this condition is satisfied the angle of applied force $\theta$ will be greater than angle of friction $\varphi$ and block can move along the plane.