Question

A gramophone record is revolving with an angular velocity $ \omega \,. $ A coin is placed at a distance $ r $ from the centre of the record .The static coefficient of friction is $ \mu $ . The coin will revolve with the record, if

• A. $ r=\mu g{{\omega }^{2}} $
• B. $ r<\frac{{{\omega }^{2}}}{\mu g} $
• C. $ r\le \frac{\mu g}{{{\omega }^{2}}} $
• D. $ r\ge \frac{\mu g}{{{\omega }^{2}}} $

Answer 1

Answer: (C)

When the disc spin, the frictional force between the gramophone record and coin is $ \mu mg. $ The coin will revolve with record, If $ {{F}_{r}}\ge {{F}_{c}} $ $ \mu mg\ge m{{\omega }^{2}}r\Rightarrow \frac{\mu g}{r}\ge {{\omega }^{2}} $