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)

Here friction force provides centripetal force so
$f=m \omega^{2} r $ but $ f \leq \mu m g$
So $m \omega^{2} r \leq \mu m g $
$\Rightarrow r \leq \frac{\mu g}{\omega^{2}}$