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JEE Main 2006 (AIEEE) · Moment of Inertia & Radius of Gyration

Moment of Inertia & Radius of Gyration question from JEE Main 2006 (AIEEE)

Q190JEE Main 2006 · AIEEEEasy

Moment of Inertia & Radius of Gyration

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

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Answer: (c)

The axis through $A$ parallel to $BD$ is at distance $\frac{l}{\sqrt{2}}$ from $B$ and $D$ , and $\sqrt{2}\,l$ from $C$ ; $A$ is on it.
$I = 2m\cdot\frac{l^2}{2} + m\cdot 2l^2$
$I = ml^2 + 2ml^2 = 3ml^2$
So the answer is (c) $3ml^2$ .

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