A ring of mass \( M \) and radius \( R \) is rotating with angular ...

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A ring of mass \( M \) and radius \( R \) is rotating with angular speed \( \omega \) about a fixed vertical axis passing through its centre \( O \) with two point masses each of mass \( \frac{M}{8} \) at rest at \( O \). These masses can move radially outwards along two massless rods fixed on the ring as shown in the figure.
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At some instant, the angular speed of the system is \( \frac{8}{9} \omega \) and one of the masses is at a distance of \( \frac{3}{5} R \) from \( O \). At this instant, the distance of the other mass from \( O \) is (2015 Adv.)
(a) \( \frac{2}{3} R \)
(b) \( \frac{1}{3} R \)
(c) \( \frac{3}{5} R \)
(d) \( \frac{4}{5} R \)
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