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 ${\omega }^1$ =

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Applying the conservation of angular momentum,
$I_1{\omega }_1=I_2{\omega }_2$
Where $I_1=m{R}^2;I_2=M{R}^2+M{R}^2+m{R}^2$
$\Rightarrow \left(m{R}^2\right)\omega =(M{R}^2+M{R}^2+m{R}^2){\omega }_2$
$\Rightarrow {\omega }_2=\frac{m\omega }{2M+m}$