Question

Four point masses, each of value $m$, are placed at the comers of square $ABCD$ of side $l$. The moment of inertia of this system about an axis passing through $A$ and parallel to $BD$ is

• A. $2\,ml^2 $
• B. $ \sqrt{3} \,ml^2 $
• C. $3\,ml^2$
• D. $ ml^2$

Answer 1

Answer: (C)

The situation is shown in figure.

$I_{x x^{\prime}} =m \times D P^{2}+m \times B Q^{2}+m \times C A^{2}$
$=m \times 2 \times\left(\frac{\sqrt{2} l}{2}\right)^{2}+m \times(\sqrt{2} l)^{2} $
$=3 \,m l^{2} $