Q105 / 197 · NEET 2009 (Mains) · Physics
A thin circular ring of mass $\mathrm{M}$ and radius $\mathrm{R}$ is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity $\omega$. If two objects each mass $m$ be attached gently to the opposite ends of a diameter of the ring, the ring, will then rotate with an angular velocity:
- A$\frac{\omega \mathrm{M}}{\mathrm{M}+\mathrm{m}}$
- B$\frac{\omega(M-2 m)}{M+2 m}$
- Correct answerC$\frac{\omega \mathrm{M}}{\mathrm{M}+2 \mathrm{~m}}$
- D$\frac{\omega(M+2 m)}{M}$
Solution
Apply conservation of angular momentum.
$$
\begin{aligned}
\mathrm{L}_{\mathrm{i}} & =\mathrm{L}_{\mathrm{f}} \\
\mathrm{MR}^2 \omega & =(\mathrm{M}+2 \mathrm{~m}) \mathrm{R}^2 \omega^{\prime} \\
\omega^{\prime} & =\frac{\mathrm{M} \omega}{\mathrm{M}+2 \mathrm{~m}}
\end{aligned}
$$
Hence, the correct answer is option: 'C'.