Question

A horizontal force $F$ is applied to a block of mass $m$ on a smooth fixed inclined plane of inclination $\theta$ to the horizontal as shown in the figure. Resultant force on the block up the plane is:

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

Answer 1

The correct option is D $F\cos \theta -mg\sin \theta$

Gravitational force acts on the block in downward direction.

Let us resolve it into parallel and perpendicular directions to the inclined plane.

Also, let us resolve the force $F$ into the parallel and perpendicular directions to the inclined plane as $F\cos \theta$ and $F\sin \theta$ respectively.

$\therefore$ Resultant upward force $F_{up}=F\cos \theta -mg\sin \theta$