Problem

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}

\frac{4g}{5a}

\frac{4g}{9a}

\frac{4g}{15a}