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 $f\le \mu mg$
So $m{\omega }^{2}r\le \mu mg$
$\Rightarrow r\le \frac{\mu g}{{\omega }^2}$