Question

Two rings each of mass ${}^{\prime }{m}^{\prime }$ and radius ${}^{\prime }{r}^{\prime }$ are placed such that their centres are at a common point and their planes are normal to each other. The moment of inertia of the system about an axis passing through the centre and perpendicular to plane of one of ring is:

• A. ${2mr}^2$
• B. ${mr}^2$
• C. $\frac{1}{2}{mr}^2$
• D. $\frac{3}{2}{mr}^2$

Answer 1

The correct option is D $\frac{3}{2}{mr}^2$

Moment of inertia of the ring about an axis perpendicular to its plane=$m{r}^2$

Moment of inertia of the ring about an axis parallel to its plane that is its diameter is $\frac{1}{2}m{r}^2$

Moment of inertia of the system is $m{r}^2+\frac{1}{2}m{r}^2=\frac{3}{2}m{r}^2$