Q. An angular ring with inner and outer radii $R_{1}$ and $R_{2}$ is roiling 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
A) $R_{1}/R_{2}$
B) 1
C) $\left( \frac{R_{1}}{R_{2}} \right)^{2}$
D) $\frac{R_{2}}{R_{1}}$
Explanation
(a) 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 the centripetal force
Dd
The force experienced by inner part $F_{1} = m\omega^{2}R_{1}$ and the force experienced by outer part, $F_{2} = m\omega^{2}R_{1}$
$\therefore\frac{F_{1}}{F_{2}} = \frac{mR_{1}\omega^{2}}{mR_{2}\omega^{2}} = \frac{R_{1}}{R_{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.