Question

A thin circular ring of mass $M$ and radius ${}^{\prime }{r}^{\prime }$ is rotating about its axis with a constant angular velocity $\omega$. Four objects each of mass $m$, are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be

• A. $\frac{M\omega }{4m}$
• B. $\frac{M\omega }{M+4m}$
• C. $\frac{(M+4m)\omega }{M}$
• D. $\frac{\left(4m\right)\omega }{(M+4m)}$

Answer 1

The correct option is B $\frac{M\omega }{M+4m}$


Applying conservation of angular momentum:-
$I_1{\omega }_1=I_2{\omega }^{\prime }$
$M{r}^2\times \omega =(M{r}^2+4m{r}^2){\omega }^{\prime }$
So, ${\omega }^{\prime }=\frac{M{r}^2\omega }{r^2(M+4m)}=\frac{M\omega }{M+4m}$