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

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

Answer 1

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

As no external toruqe is acting about the axis, angular momentum of system remains conserved.
$I_1{\omega }_1=I_2{\omega }_2$
$\Rightarrow {\omega }_2=\frac{I_1{\omega }_1}{I_2}=\frac{M{r}^2\omega }{(M+2m)r^2}=\frac{M\omega }{M+2m}$