Question

A gramophone recorder rotates at angular velocity of $\omega$ a coin is kept at a distance $r$ from its centre. If $\mu$ is static friction constant then coil will rotate with gramophone if:

• A. $r>\mu g>{\omega }^2$
• B. $r=\mu g/{\omega }^2$ only
• C. $r\le \mu g/{\omega }^2$
• D. $r<\mu /{\omega }^2$

Answer 1

The correct option is C $r\le \mu g/{\omega }^2$

Given that,

Angular velocity = $\omega$

Distance = $r$

Static friction = $\mu$

Now, the coin will revolve with record if

Frictional force ≥ centripetal force

$F_f\ge F_{centripetal}$

$\mu mg\ge m{\omega }^{2}r$

$\frac{\mu g}{{\omega }^2}\ge r$

Hence, the coin will rotate with gramophone if $\frac{\mu g}{{\omega }^2}\ge r$