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 $F_r\ge F_c$ $\mu mg\ge m{\omega }^{2}r\Rightarrow \frac{\mu g}{r}\ge {\omega }^2$