Question

Two rings of the same radius and same mass 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 centre and perpendicular to the plane of one of the rings is (mass of the ring $=m$, radius $=r$ ) :

• A. $\frac{5}{2}m{r}^2$
• B. $m{r}^2$
• C. $\frac{3}{2}m{r}^2$
• D. $2m{r}^2$

Answer 1

Answer: (A), (C)

$\frac{5}{2}m{r}^2$
$\frac{3}{2}m{r}^2$

MI of the ring about an axis which is perpendicular to the plane of the ring is $I=m{R}^2$
MI of the ring about about an axis which is diameter is $I^{\prime }=\frac{m{R}^2}{2}$
$I_{total}=m{r}^2+\frac{m{r}^2}{2}$ (considering the whole as one system)
$=\frac{3}{2}m{r}^2$