Question

Two uniform rings of same radius $r$ and mass $m$ are placed such that their centres are at a common point and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the centres and perpendicular to plane of one of the rings is:

• A. $\frac{1}{2}m{r}^2$
• B. $m{r}^2$
• C. $\frac{3}{2}m{r}^2$
• D. $2m{r}^2$

Answer 1

The correct option is C

$\frac{3}{2}m{r}^2$

Moment of inertia of the system $I=I_1+I_2$
$I_1=m{r}^2=$ moment of inertia of a ring about an axis passing through centre and perpendicular to the plane
$I_2=$ moment of inertia about one of the diameters for the second ring$=\frac{1}{2}m{r}^2$
$\therefore I=I_1+I_2=\frac{3}{2}m{r}^2$