When a body slides down on inclined plane with coefficient of friction \(\mu\), then its acceleration will be

1. \(g(\sin \theta-\mu \cos \theta)\)
2. \(g(\sin \theta+\mu \cos \theta)\)
3. \(g(\mu \sin \theta-\cos \theta)\)
4. \(g \mu(\sin \theta-\cos \theta)\)

Solution

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, \(\begin{aligned} \Rightarrow & & m a & =m g \sin \theta-\mu R \\ \Rightarrow & & m a & =m g \sin \theta-\mu m g \cos \theta \\ \Rightarrow & & a & =g \sin \theta-\mu g \cos \theta \\ \Rightarrow & & a & =g(\sin \theta-\mu \cos \theta) \end{aligned}\)

Asked in: AP EAMCET 2020 (17 Sep Shift 1)

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