A gramophone record is revolving with angular velocity $ω$ . A coin is placed at a distance $r$ from the centre of the record. The static coefficient of friction is $μ$ . The coin will revolve with the record if

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Solution

Here friction force provides centripetal force so,

$f = m ω^{2} r but f \leq μ m g$

$∴ m ω^{2} r \leq μ m g$

$\Rightarrow r \leq \frac{μ g}{ω^{2}}$

Hence, $(C)$ is the correct answer.

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