A solid cylinder is rolling down on an inclined plane of angle . … - Vidyadip

MCQ

A solid cylinder is rolling down on an inclined plane of angle $\theta $. The coefficient of static friction between the plane and the cylinder is $\mu _s$. The condition for the cylinder not to slip is

A
$\tan \,\theta \, \geq \,\,3\,{\mu _s}$
B
$\tan \,\theta \, > \,\,3\,{\mu _s}$
✓
$\tan \,\theta \, \leq \,\,3\,{\mu _s}$
D
$\tan \,\theta \, < \,\,3\,{\mu _s}$

✓

Answer

Correct option: C.

$\tan \,\theta \, \leq \,\,3\,{\mu _s}$

c
$\mu_{\mathrm{s}} \geq \frac{\tan \theta}{1+\mathrm{R}^{2} / \mathrm{K}^{2}} \Rightarrow \mu_{\mathrm{s}} \geq \frac{\tan \theta}{1+2} \rightarrow \tan \theta \leq 3 \mu_{\mathrm{s}}$

$\frac{\mathrm{K}^{2}}{\mathrm{R}^{2}}=\frac{1}{2}(\text { solid cylinder })$

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