Initial angular velocity of a circular disc of mass $M$ is $\omega_1$. Then two small spheres of mass $m$ are attached gently to diametrically opposite points on the edge of the disc. What is the final angular velocity of the disc?\\
(1) $\left( \frac{M+m}{M} \right) \omega_1$\\
(2) $\left( \frac{M+m}{m} \right) \omega_1$\\
(3) $\left( \frac{M}{M+4m} \right) \omega_1$\\
(4) $\left( \frac{M}{M+2m} \right) \omega_1$