Question

Four identical thin rods each of mass $m$ and length $L$ are joined together to form a square frame. The moment of inertia of this frame about an axis passing through any one side of the frame is:

• A. $\frac{2m{L}^2}{3}$
• B. $\frac{m{L}^2}{6}$
• C. $\frac{5m{L}^2}{3}$
• D. $\frac{7m{L}^2}{6}$

Answer 1

Answer: (C)

$\frac{5m{L}^2}{3}$

Using $I=m{r}^2$ we see that the moment of inertia of the rod through which the rotational axis is passing would be zero and that which is parallel to it would be $I=m{L}^2$

For the other rods we have the moment of inertia passing through an end as $I=\frac{m{L}^2}{3}$

Thus we get the total moment of inertia as

$0+m{L}^2+(2\times \frac{m{L}^2}{3})=\frac{5}{3}m{L}^2$