Question

Three rings, each of mass $m$ and radius $r$, are so placed that they touch each other. Find the moment of inertia about the axis as shown in figure.

• A. $5m{r}^2$
• B. $\frac{5}{7}m{r}^2$
• C. $7m{r}^2$
• D. $\frac{7}{2}m{r}^2$

Answer 1

The correct option is D $\frac{7}{2}m{r}^2$

Given,

Mass $m$ and radius $R$

Moment of inertia at lateral axis, $I=\frac{m{r}^2}{2}$

Moment of inertia at edge of ring, $I=\frac{m{r}^2}{2}+m{r}^2=\frac{3m{r}^2}{2}$

There is two ring at connect with edge and one is connected at center of ring

$I=\frac{m{r}^2}{2}+2\times \frac{3m{r}^2}{2}=\frac{7}{2}m{r}^2$

Hence, total inertia of system is $\frac{7}{2}m{r}^2$