• # question_answer Consider a small cube of mass m kept on a horizontal disc. If the disc is to rotate with uniform angular velocity, what could be its maximum vlaue without causing any sliding between the cube and (Coefficient of static friction between cube and disc is $\mu$). A)  $\sqrt{\frac{\mu g}{r}}$                  B)  $\sqrt{\frac{2\mu g}{2}}$C)  $\sqrt{\frac{\mu g}{2r}}$                     D)  $2\sqrt{\frac{\mu g}{r}}$

In absence of any sliding, net force on the cube in the frame of reference rotating with disc, will be zero. We find two forces in the plane of disc-frictional force and centrifugal force. Hence,  $M{{w}^{2}}f=1$ But  $f\le \mu \,mg$ Hence, $w\le \sqrt{\mu g/r}$ $\Rightarrow$            $w\le \sqrt{\mu g/r}$ $\Rightarrow$            ${{w}_{\max }}=\sqrt{\frac{\mu g}{r}}$