Q. A solid cylinder is rolling down on an inclined plane of angle $\theta$. The coefficient of static fraction between the plane and cylinder is $\mu_{s}$. Then condition for the cylinder not to slip is
A) $\tan{\theta\ \geq 3\mu_{s}}$
B) $\tan{\theta > 3\mu_{s}}$
C) $\tan{\theta\ \geq 3\mu_{s}}$
D) $\tan{\theta < 3\mu_{s}}$
Explanation
(c) For the rolling a solid cylinder acceleration $a = \frac{g}{3}\sin\theta$
[image:7_image119.emf]
$\therefore$ The condition for the cylinder to remain in equilibrium
$Ma \leq \mu\ sR$
$\Rightarrow$ $\frac{1}{2}Mg\sin{\theta \leq Mg\cos{\theta.\mu_{s}}}$
or $\mu_{s} \geq \frac{1}{3}\tan\theta$
or $\tan{\theta \leq 3\ \mu_{s}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.