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

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$r = \frac{μ g}{ω^{2}} only$

$r > \frac{μ g}{ω^{2}} only$

$r \leq \frac{μ g}{ω^{2}} only$

$r < \frac{μ g}{ω^{2}} only$

answer is D.

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Detailed Solution

$\begin{array}{l} N o s l i p c o n d i t i o n \\ μ m g \geq m ω^{2} r \\ \Rightarrow μ g \geq r ω^{2} \\ \Rightarrow r \leq \frac{μ g}{ω^{2}} \end{array}$

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