Question

An annular ring with inner and outer radii $ {{R}_{1}} $ and $ {{R}_{2}} $ is rolling without slippling 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, $ \frac{{{F}_{1}}}{{{F}_{2}}} $ is

• A. 1
• B. $ \left( \frac{{{R}_{1}}}{{{R}_{2}}} \right) $
• C. $ \frac{{{R}_{2}}}{{{R}_{1}}} $
• D. $ {{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{2}} $

Answer 1

Answer: (B)

Let panicle $ A $ is situated on the inner part and $ B $ on the outer part of the ring. As the ring is moving with uniform angular speed therefore, both particles will feel centrifugal force.
$ \therefore $ $ \frac{{{F}_{1}}}{{{F}_{2}}}=\frac{{{F}_{A}}}{{{F}_{B}}}=\frac{m{{\omega }^{2}}{{R}_{1}}}{m{{\omega }^{2}}{{R}_{2}}} $ $ \Rightarrow $ $ \frac{{{F}_{1}}}{{{F}_{2}}}=\frac{{{R}_{1}}}{{{R}_{2}}} $