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A gramophone record is revolving with 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

1. \(r = \mu g \omega^2\)
2. \(2rg\omega\mu = 1\)
3. \(2g r \mu \omega \le 1\)
4. \(2g r \mu \omega \ge 1\)

Correct answer: \(2g r \mu \omega \le 1\)

Solution

The coin moves with the record only if static friction can provide the needed centripetal force. Thus, \(mr\omega^2 \le \mu mg\), which gives the condition on \(r\), \(\mu\), and \(\omega\).

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