An annular ring with inner and outer radii $R_{1} a n d R_{2}$ is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situates on the inner and outer parts of the rings $F_{1} / F_{2}$ is :

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R_{1} / R_{2}

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R / R_{1}

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(R_{1} / R_{2})^{2}

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Solution

The correct option is B $R_{1} / R_{2}$
Consider a rolling without slipping case where $a_{c m} = o$ and the ring rolls by angular velocity $W$ .
The point $A$ & $B$ experience only centripetal force given by : $F_{1} = m R_{1} W^{2}$ and $F_{2} = m R_{2} W^{2}$
Thus ratio, $\frac{F_{1}}{F_{2}} = \frac{R_{1}}{R_{2}}$

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