An annular ring with inner and outer radii R_ | vedclass

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(B) For a particle of mass $m$ rotating in a circle of radius $r$ with a uniform angular speed $\omega$,the centripetal force is given by $F = m \omeg

Vedclass · Accepted Answer

$\frac{R_{1}}{R_{2}}$

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(B) For a particle of mass $m$ rotating in a circle of radius $r$ with a uniform angular speed $\omega$,the centripetal force is given by $F = m \omega^{2} r$.For the particle on the inner part of the ring at radius $R_{1}$,the centripetal force is $F_{1} = m \omega^{2} R_{1}$.For the particle on the outer part of the ring at radius $R_{2}$,the centripetal force is $F_{2} = m \omega^{2} R_{2}$.Taking the ratio of these two forces:$\frac{F_{1}}{F_{2}} = \frac{m \omega^{2} R_{1}}{m \omega^{2} R_{2}} = \frac{R_{1}}{R_{2}}$.Thus,the ratio of the forces is $\frac{R_{1}}{R_{2}}$.

An annular ring with inner and outer radii $R_{1}$ and $R_{2}$ is rotating with a uniform angular speed $\omega$ about its central axis. The ratio of the centripetal forces experienced by two particles of equal mass $m$ situated on the inner and outer parts of the ring,$\frac{F_{1}}{F_{2}}$ is

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