Q. 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) $r \geq \frac{\mu g}{\omega^{2}}$
B) $r = \mu g\omega^{2}$
C) $r < \frac{\omega^{2}}{\mu g}$
D) $r \leq \frac{\mu g}{\omega^{2}}$
Explanation
(d) Here friction force provides centripetal force so
$f = m\ \omega^{2}\ r$ but $f \leq \mu mg$
So $m\omega^{2}r \leq \mu mg \Rightarrow r \leq \frac{\mu g}{\omega^{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.