Question

When a body slides down an inclined plane with coefficient of friction $\mu$, then its acceleration will be:

• A. $g(\sin \theta -\mu \cos \theta )$
• B. $g(\sin \theta +\mu \cos \theta )$
• C. $g(\mu \sin \theta -\cos \theta )$
• D. $g\mu (\sin \theta -\cos \theta )$

Answer 1

Answer: (A)

When a body of mass $m$ slides down on inclined plane with acceleration $a$, then various forces acting on the body are shown in the figure.

According to Newton's second law of motion, $ma=mg\sin \theta -\mu R$
$\Rightarrow ma=mg\sin \theta -\mu mg\cos \theta$
$\Rightarrow a=g\sin \theta -\mu g\cos \theta$
$\Rightarrow a=g(\sin \theta -\mu \cos \theta )$