Question

A thin circular ring of mass $m$ and radius $R$ is rotating about its axis with a 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 an angular velocity ${\omega }^{\prime }=$

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

Answer 1

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

using conservation of Angular momentum inertia angled momentum : final Angular momentum

$I{w}^{\prime }=I^{\prime }{w}^{\prime }$

$m{R}^{2}w=(m{R}^2+M{R}^2+M{R}^2)w^1$

$m{R}^{2}w=(m{R}^2+2M{R}^2)w^1$

$\therefore w^1=\frac{mw}{m+2m}$ Answer is $A$