A thin circular ring of mass M and radius R is rotating with a constant angular velocity 2 $\mathrm{rads}^{-1}$ in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two objects each of mass m be attached gently to the opposite ends of a diameter of ring, the ring will then rotate with an angular velocity (in rads-1).
Select the correct option:
A
$\frac{\mathrm{M}}{(\mathrm{M}+\mathrm{m})}$
B
$\frac{(\mathrm{M}+2 \mathrm{~m})}{2 \mathrm{M}}$
C
$\frac{2 \mathrm{M}}{(\mathrm{M}+2 \mathrm{~m})}$
D
$\frac{2(\mathrm{M}+2 \mathrm{~m})}{\mathrm{M}}$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
Applying conservation of angular momentum
$$
\begin{aligned}
& M R^2 \omega=\left(M R^2+2 m R^2\right) \omega^{\prime} \\
& \omega^{\prime}=\frac{2 M}{M+2 m}
\end{aligned}
$$
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