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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
$r \leq \frac{\mu g}{\omega^2}$
Detailed Solution
For the coin to go round with the record, it needs a centripetal force $mr\omega^2$ towards the centre.
This force is provided by static friction, whose maximum value is $\mu mg$.
The coin does not slip as long as the required force does not exceed the maximum friction: $mr\omega^2 \leq \mu mg$
$r\omega^2 \leq \mu g$
$r \leq \frac{\mu g}{\omega^2}$
This force is provided by static friction, whose maximum value is $\mu mg$.
The coin does not slip as long as the required force does not exceed the maximum friction: $mr\omega^2 \leq \mu mg$
$r\omega^2 \leq \mu g$
$r \leq \frac{\mu g}{\omega^2}$