Question

A block of mass $m$ is at rest on a rough wedge of angle $\theta$ as shown. What is the force exerted by the wedge on the block?

• A. $mg\cos \theta$
• B. $mg\sin \theta$
• C. $mg\tan \theta$
• D. $mg$

Answer 1

The correct option is D $mg$

The forces acting on the block are:-
a) Its weight, $mg$
b) Contact force between the wedge and the block which is the resultant of normal reaction and
(c) Frictional force.

Since the block is at rest, forces along the inclined plane are balanced. Also the forces perpendicular are balanced as shown in figure.
$f=mg\sin \theta$
$N=mg\cos \theta$
Net force exerted by wedge on the block is $\sqrt{N^2+f^2}=mg$