• # question_answer 5) A heavy circular disc whose plane is vertical is kept at rest on a rough inclined plane by a string parallel to the plane and touching the disc as shown in the figure. The disc starts to slip if: A) $\mu <\frac{1}{2}\tan \alpha$                    B) $\mu >\frac{1}{2}\tan \alpha$C) $\mu <\tan \alpha$               D) $\mu >\tan \alpha$

Correct Answer: A

Solution :

For rotational equilibrium, net torque is 0. Taking torque about the center of Disc,$Tr=fr$or $T=f.$ For slipping $T+f<mg\,\sin \alpha$ or $2f<mg\sin \alpha$ or $2\mu \,mg\,\cos \alpha <mg\sin \alpha$ or $\mu <\frac{1}{2}\tan \alpha$ Hence, the correction option is [a].

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