A thin circular ring of mass $M$ and radius $R$ rotates about an axis through its centre and perpend

Question

A thin circular ring of mass $M$ and radius $R$ rotates about an axis through its centre and perpendicular to its plane, with a constant angular velocity $\omega$. Four small spheres each of mass m (negligible radius) are kept gently to the opposite ends of two mutually\ perpendicular diameters of the ring. The new angular velocity of the ring will be.\

Professor PC Thomas Classes · Answer

A) By the law of conservation of angular momentum, $\mathrm{I}_{1} \omega_{1}=\mathrm{I}_{2} \omega_{2}$\ $\mathrm{MR}^{2} \omega_{1}=(\mathrm{M}+4 \mathrm{~m}) \mathrm{R}^{2} \omega_{2}$\ $	herefore \omega_{2}=\frac{M}{(M+4 m)} \omega_{1}=\left(\frac{M}{M+4 m}ight) \omega$\