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) $\sqrt{3}\ ml^{2}$
B) $3\ ml^{2}$
C) $ml^{2}$
D) $2\ ml^{2}$
Explanation
(b) $r_{2} = r_{4} = OA = \frac{l}{\sqrt{2}}$ and $r_{3} = l\sqrt{2}$
Moment of inertia of the system about given axis
$I{= I}_{1} + I_{2} + I_{3} + I_{4}$
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$\Rightarrow I = 0 + m\left( r_{2} \right)^{2} + m\left( r_{3} \right)^{2} + m\left( r_{4} \right)^{4}$
$\Rightarrow I = m\left( \frac{l}{\sqrt{2}} \right)^{2} + m\left( l\sqrt{2} \right)^{2} + m\left( \frac{l}{\sqrt{2}} \right)^{2}\ \therefore I = 3ml^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.