Question

Two rings of same radius $\left(r\right)$ and mass $\left(m\right)$ are placed such that their centers 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 centre and perpendicular to plane of one of the ring 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 $\frac{3}{2}m{r}^2$

From the above figure the $I_{A{A}^{\prime }}$

$I_{A{A}^{\prime }}=m{r}^2+\frac{m{r}^2}{2}⟹I_{A{A}^{\prime }}=\frac{3}{2}m{r}^2$

Hence Option C is correct