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A thin circular ring of mass $M$ and radius $r$ is rotating about its axis with an angular speed $\omega$. Two particles having mass $m$ each are now attached at diametrically opposite points. The angular speed of the ring will become:
(1) $\omega\frac{M}{M+m}$
(2) $\omega\frac{M+2m}{M}$
(3) $\omega\frac{M}{M+2m}$
(4) $\omega\frac{M-2m}{M+2m}$
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