Question

A block of mass m is placed on a smooth inclined plane of inclination θ with horizontal. The force exerted by the plane on the block has a magnitude:

• A. $mg$
• B. $\frac{mg}{\cos \theta }$
• C. $mg\cos \theta$
• D. $mg\tan \theta$

Answer 1

The correct option is C

$mg\cos \theta$

1. This question uses the third law of motion.
2. According to Newton's Third law of motion, ‘Every action has an equal and opposite reaction’.
3. The block exerts a force of $mg\cos \theta$. The inclined plane exerts a reaction force on the block which is equal to $mg\cos \theta$ by magnitude, in the opposite reaction.
   

Wrong option:

1. mg: The option mg is downward, not perpendicular to the inclined plane, thus, can't be the force exerted by the inclined plane.
2. $\frac{mg}{\cos \theta }$ is the wrong answer.
3. $mg\tan \theta$ is the wrong answer.

Thus, the plane exerts a force $\mathit{m}\mathit{g}\mathit{c}\mathit{o}\mathit{s}\mathit{\theta }$ on the block.

Hence, the correct option is Option C.