Question

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

• A. $ \tan \,\theta \ge \,3\mu_{s}$
• B. $ \tan \,\theta >3\mu _{s}$
• C. $ \tan \,\theta \le 3\mu _{s}$
• D. $ \tan \,\theta < 3\mu_{s}$

Answer 1

Answer: (C)

For the rolling of a solid cylinder acceleration
$a=\frac{g}{3} \sin \theta$
$\therefore $ The condition for the cylinder to remain in equilibrium
$m a \leq \mu_{s} R$
$\Rightarrow \frac{1}{3} M g \sin \theta \leq M g \cos \theta \cdot \mu_{s}$
or $\mu_{s} \geq \frac{1}{3} \tan \theta$
or $\tan \theta \leq 3\, \mu_{s}$