A thin circular ring of Mass $M$ and radius $r$ is rotating about its axis with a constant angular velocity…
A thin circular ring of Mass $M$ and radius $r$ is rotating about its axis with a constant angular velocity $\omega$. Four objects each of mass $m$, are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be:
$\frac{M \omega}{4 m}$
$\frac{M \omega}{M+4 m}$
$\frac{(M+4 m) \omega}{M}$
$\frac{(M-4 m) \omega}{M+4 m}$
Solution
According to law of conservation of angular momentum
$\begin{aligned}
& M r^2 \omega=\left(M r^2+4 m r^2\right) \omega^{\prime} \\
& \Rightarrow \omega^{\prime}=\frac{M \omega}{M+4 m}
\end{aligned}$