Question

A block of mass $m$ is at rest on a rough inclined plane of angle of inclination $\theta$. If coefficient of friction between the block and the inclined plane is $\mu$, then the minimum value of force along the plane required to move the block on the plane is:

• A. $mg[\mu \cos \theta -\sin \theta ]$
• B. $mg[\sin \theta +\mu \cos \theta ]$
• C. $mg[\mu \cos \theta +\sin \theta ]$
• D. $mg[\sin \theta -\mu \cos \theta ]$

Answer 1

The correct option is A $mg[\mu \cos \theta -\sin \theta ]$

required force F will act along Fs (force due to static friction) and in opposite direction will be mgsinθ

"along the plane" means the block is moving upwards

"down the plane" mean the block is moving downwards

so for upwards

$F=Fs-mgsin\theta =\mu mgcos\theta -mgsin\theta$

$=mg(\mu cos\theta -sin\theta )$

Hence,

option $A$ is correct answer.