Question

$I$ is moment of inertia of a thin square plate about an axis passing through any side. This square plate is bent into hollow cylinder such that two parallel sides of plate just come in contact. The moment of inertia of cylinder about an axis parallel to its axis and touching its surface is:

• A. $\frac{3I}{{\pi }^2}$
• B. $\frac{2I}{{\pi }^2}$
• C. $\frac{3I}{2{\pi }^2}$
• D. $\frac{2I}{3{\pi }^2}$

Answer 1

Answer: (C)

$\frac{3I}{2{\pi }^2}$

Let mass of square plate be $M$ and side be $L$.

So MI about axis passing through one of its side is $M{L}^2/3=I$

Now when it is bend into a hollow cylinder, its mass remain same as $M$ and radius is given as $2\pi r=L\Rightarrow r=L/2\pi$

So MI about axis touching its surface is $2M{r}^2=2M{L}^2/4{\pi }^2=\left(M{L}^2/3\right)\times \left(3/2{\pi }^2\right)=3I/2{\pi }^2$