Question

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

• A. $\frac{g}{3a}$
• B. $\frac{4g}{5a}$
• C. $\frac{4g}{9a}$
• D. $\frac{4g}{15a}$

Answer 1

Answer: (D)

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

For the particle not to move, friction force balances the centrifugal force.

$mr{w}^2=f$ where $r=\frac{5a}{4}$, $f=\mu mg$

$m\frac{5a}{4}{w}^2=\frac{1}{3}mg$

$⟹w^2=\frac{4g}{15a}$