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 of the ring,\[\frac{{{F}_{1}}}{{{F}_{2}}}\]is     AIEEE  Solved  Paper-2005

A) \[\frac{{{R}_{2}}}{{{R}_{1}}}\]    

B)        \[{{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{2}}\]           

C)        1                             

D)        \[\frac{{{R}_{1}}}{{{R}_{2}}}\]

Correct Answer: D

Solution :

Since,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. The force experienced by inner part,and the force experienced by outer part, \[\therefore \,\,\,\frac{{{F}_{1}}}{{{F}_{2}}}\,=\frac{m{{\omega }^{2}}{{R}_{1}}}{m{{\omega }^{2}}{{R}_{2}}}=\frac{{{R}_{1}}}{{{R}_{2}}}\]