Question

A thin circular ring of mass $M$ and radius $r$ is rotating about its axis with constant angular velocity $\omega$. Two objects each of mass $m$ are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with angular velocity given by
$\text{[Main-2010]}$

• A. $\frac{(M+2m)\omega }{M}$
• B. $\frac{2M\omega }{M+2m}$
• C. $\frac{M\omega }{M+2m}$
• D. $\frac{(M+2m)\omega }{2m}$

Answer 1

The correct option is C $\frac{M\omega }{M+2m}$

Applying conservation of angular momentum,
$I_1{\omega }_1=I_2{\omega }_2$

$\Rightarrow M{R}^2\omega =(M+2m)R^2{\omega }^{\prime }$
$\begin{array}{c}{\omega }^{\prime }=\frac{m\omega }{(M+2m)}\end{array}$

Hence, option $\left(D\right)$ is correct.