Question

Three rings each of mass, m and radius, r are placed in a plane touching each other as shown. The radius of gyration of the system about the axis as shown in the figure is

• A. $\sqrt{\frac{7}{6}}r$
• B. $\sqrt{\frac{5}{3}}r$
• C. $\sqrt{\frac{5}{6}}r$
• D. $\sqrt{\frac{7}{2}}r$

Answer 1

The correct option is A $\sqrt{\frac{7}{6}}r$

Moment of inertia of the system about the given axis, $I=I_1+I_2+I_3$
$I_1=\frac{m{r}^2}{2},I_2=I_3=\frac{3}{2}m{r}^2,\therefore I=I_1+I_2+I_3=\frac{7}{2}m{r}^2$
Also, moment of inertia, $I=3m{k}^2$, where k is radius of gyration.
$\therefore 3m{k}^2=\frac{7}{2}m{r}^2\Rightarrow k=\sqrt{\frac{7}{6}}r$