An angular ring with inner and outer radii  $R_{1}and{R}_2$ is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring.  $F_1/F_{2}is$

$Since\omega$ is constant, v would also be constant, so, no net force or torque is acting on ring. The force experienced by any particle is only along radial direction or we can say it the centripetal force.

The force experienced by inner part, $F_1=m{\omega }^2{R}_1^2$ and the force experience by outer part, $F_2=m{\omega }^2{R}_1$

$\therefore \frac{F_1}{F_2}=\frac{m{R}_1{\omega }^2}{m{R}_2{\omega }_2}=\frac{R_1}{R_2}$