Question

The moment of inertia of a rod about an axis through its centre and perpendicular to it is $\frac{1}{12}M{L}^2$ (where $M$ is the mass and $L$, the length of the rod). The rod is bent in the middle so that the two halts make an angle of ${60}^{\circ }$. The moment of inertia of the bent rod about the same axis would be

• A. $\frac{1}{48}M{L}^2$
• B. $\frac{1}{12}M{L}^2$
• C. $\frac{1}{24}M{L}^2$
• D. $\frac{M{L}^2}{8\sqrt{3}}$

Answer 1

Answer: (B)

$\frac{1}{12}M{L}^2$

We know that for a body, moment of inertia $M.I=\sum M{r}^2$
Now, bending of rod does not alter the distribution of individual particle, the body is made of, so the value of $\sum M{r}^2$ will not change. Hence the changed moment of inertia of the body will be $\frac{1}{12}M{L}^2$.