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, $m a=m g \sin \theta-\mu R$
$\Rightarrow m a=m g \sin \theta-\mu m g \cos \theta$
$\Rightarrow a=g \sin \theta-\mu g \cos \theta$
$\Rightarrow a=g(\sin \theta-\mu \cos \theta)$