A block of mass $m$ rests on a rough inclined plane. The coefficient of friction between the surface and the block is $\mu$. At what angle of inclination $\theta$ of the plane to the horizontal will the block just start to slide down the plane?
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The various forces acting on the block are as shown in the figure.
From figure
$\operatorname{mgsin} \theta=\mathrm{f}$ $...(i)$
$\mathrm{mg} \cos \theta=\mathrm{N}$ $...(ii)$
Divide $(i)$ by $( ii),$ we get
$\tan \theta=\frac{\mathrm{f}}{\mathrm{N}}=\frac{\mu \mathrm{N}}{\mathrm{N}}$
or $\theta=\tan ^{-1}(\mu)$
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