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Q.

A gramophone record is revolving with an 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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a

r $\geq \frac{μ g}{ω^{2}}$

b

r $\leq \frac{μ g}{ω^{2}}$

c

r < $\frac{ω^{2}}{μ g}$

d

$r = μ g ω^{2}$

answer is C.

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Detailed Solution

detailed_solution_thumbnail

When the disc spins the frictional force between the gramophone record and coin is $μ m g$

The coin will revolve with record, if

$F_{f r i c t i o n a l} \geq F_{c e n t r i p e t a l}$

$μ m g \geq m ω^{2} r$

$\frac{μ g}{r} \geq ω^{2}$

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A gramophone record is revolving with an 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