Q. Four point masses, each of value $m$, are placed at the corners of a 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) ${ml}^{2}$
Explanation
(c) The situation is shown in figure
$I_{XX^{''}} = m \times DP^{2} + m \times BQ^{2} + m \times CA^{2}$
[image:7_image139.emf]
$= m \times 2 \times \left( \frac{\sqrt{2}l}{2} \right)^{2} + m \times \left( \sqrt{2}l \right)^{2}$
$= 3ml^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.