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 the diameter of the ring. The wheel now rotates with an angular velocity

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

Answer 1

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

Let the final angular velocity be $w^{\prime }.$

Angular momentum is conserved about center of the ring.

$L_i=L_f$

$Iw+0=I{w}^{\prime }+2\times m{r}^2{w}^{\prime }$

$M{r}^{2}w+0=M{r}^2{w}^{\prime }+2\times m{r}^2{w}^{\prime }$

$⟹w^{\prime }=\frac{Mw}{M+2m}$