Question

Two rings of the same mass and radius 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 at one of the rings is (Take M- mas of each ring and R= radius of each ring)

• A. $M{R}^2$
• B. $\frac{3}{2}M{R}^2$
• C. $2M{R}^2$
• D. $\frac{5}{2}M{R}^2$

Answer 1

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

MI of the ring about an axis passing through the centre of the ring and in the plane of the ring is $\frac{M{R}^2}{2}$.
MI of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is $M{R}^2$.
$\therefore$ $I=\frac{M{R}^2}{2}+M{R}^2=\frac{3}{2}M{R}^2$