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) $\omega \frac { M + 2 m } { M }$
(3) $\omega \frac { M } { M + 2 m }$
(4) $\omega \frac { M - 2 m } { M + 2 m }$