Question

The rings of the same radius $R$ and mass $m$ are placed such that their centers are at the common point and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the center and perpendicular to the 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 $\frac{3}{2}m{r}^2$

MOI of the system=MOI of the ring rotating about an axis perpendicular to its plane+ MOI of ring rotating about an axis in its own plane

$MOI=m{r}^2+\frac{1}{2}m{r}^2=\frac{3}{2}m{r}^2$