Four point masses, each of value $\mathrm{m}$, are placed at the corners of a square $A B C D$ of side…

Four point masses, each of value $\mathrm{m}$, are placed at the corners of a square $A B C D$ of side $\ell$. The moment of inertia through $A$ and parallel to $B D$ is
  1. $\mathrm{m} \ell^2$
  2. $2 \mathrm{~m} \ell^2$
  3. $3 m \ell^2$
  4. $3 \mathrm{~m} \ell^2$

Solution

$\mathrm{I}=2 \mathrm{~m}(\ell / \sqrt{2})^2=3 \mathrm{~m} \ell^2$

Asked in: JEE Main 2006

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