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 = 3mk², where k is radius of gyration.
$\therefore 3m{k}^2=\frac{7}{2}m{r}^2\Rightarrow k=\sqrt{\frac{7}{6}r}$