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A rough horizontal plate rotates with angular velocity $ω$ about a fixed vertical axis. A particle of mass m lies on the plate at a distance $\frac{5 a}{4}$ from this axis. The coefficient of friction between the plate and the particle is $\frac{1}{3}$ . The largest value of $ω^{2}$ for which the particle will continue to be at rest on the revolving plate is

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$\frac{4 g}{5 a}$

$\frac{4 g}{9 a}$

$\frac{4 g}{15 a}$

$\frac{g}{3 a}$

answer is D.

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Detailed Solution

$μ m g = m R ω^{2}$

$∴ ω^{2} = \frac{μ g}{R} = \frac{(1 / 3) g}{5 a / 4} = \frac{4 g}{15 a}$

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