Question

A thin circular ring of mass M and radius R is rotating about its fixed axis with a constant angular velocity . Two objects each of mass m, are attached gently to the opposite ends of a dismeter of the ring. The ring now rotates with an angular velocity.

• A. $\frac{\omega M}{(M+m)}$
• B. $\frac{\omega M}{(M+2m)}$
• C. $\frac{\omega M}{(M-2m)}$
• D. $\frac{\omega (M+3m)}{M}$

Answer 1

The correct option is B $\frac{\omega M}{(M+2m)}$

$\begin{array}{c}\text{Initial Moment of Inertia If}M{R}^2\\ {\text{Final moment of Inertia I}}_2=(M+2m)R^2\\ \text{Let the Final angular velocity be (w')}\end{array}$

By conservation of angular momentum- $\begin{array}{cc}{I}_1& \omega =I_2{\omega }^{\prime }\\ & \Rightarrow W^{\prime }=\frac{I_1\omega }{I_2}=\frac{M{R}^2\omega }{(M+2m)R^2}\\ {\omega }^{\prime }& =\frac{M\omega }{M+2m}\end{array}$

Henu, option (B) is correct.