Question

Two rings of the same radius $R$ and mass $M$ are placed such that their centres coincide and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the common centre and perpendicular to the plane of one of the rings is:

• A. $\frac{M{R}^2}{2}$
• B. $M{R}^2$
• C. $\frac{3M{R}^2}{2}$
• D. $2M{R}^2$

Answer 1

The correct option is C $\frac{3M{R}^2}{2}$

The MI of first ring for which axis is perpendicular to its plane is $M{R}^2$

The MI of second ring for which axis is in its plane is $M{R}^2/2$

So total MI of two-ring system is $M{R}^2+M{R}^2/2=3M{R}^2/2$