• # question_answer             An annular 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 F of the ring, $\frac{{{F}_{1}}}{{{F}_{2}}}$is A)  1                     B)   $\frac{{{R}_{1}}}{{{R}_{2}}}$                C) $\frac{{{R}_{2}}}{{{R}_{1}}}$                D)   ${{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{2}}$

Let particle A be situated on the inner part and B on the outer part of the ring. As the ring is moving with uniform angular speed, so their angular accelerations are zero, therefore both the particles will experience centrifugal force only. $\frac{{{F}_{1}}}{{{F}_{2}}}=\frac{m{{\omega }^{2}}{{R}_{1}}}{m{{\omega }^{2}}{{R}_{2}}}=\frac{{{R}_{1}}}{{{R}_{2}}}$ Hence, the correction option is (b).