Question

Two thin uniform circular rings each of radius $10m$ and mass $0.1kg$ are arranged such that they have Common centre and their planes are perpendicular to each other. The M.I. of the system about an axis passing through their common centre and perpendicular to the plane of either of the ring in $kg{m}^{-2}$ is:

• A. $1.5$
• B. $4.5$
• C. $15$
• D. $18$

Answer 1

The correct option is C $15$

The moment of inertia of the ring about the diameter is given as,

$I_d=\frac{1}{2}m{r}^2$

The moment of inertia of the ring about the axis perpendicular to the plane is given as,

$I_p=m{r}^2$

The moment of inertia of the system about an axis passing through their common centre and perpendicular to the plane of either of the ring is given as,

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

$I=\frac{3}{2}\times 0.1\times {\left(10\right)}^2$

$I=15kg/m^2$