Question 59 of 280

Four equal masses, $m$ each are placed at the corners of a square of length $\left(l\right)$ as shown in the figure. The moment of inertia of the system about an axis passing through $A$ and parallel to $DB$ would be :

A$m{l}^{2}$B$2m{l}^{2}$C$3m{l}^{2}$D$\sqrt{3}m{l}^{2}$

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Answer: (C) $3m{l}^{2}$

Moment of inertia of point mass $=$ mass $\times$ ${\left(Perpendiculardistancefromaxis\right)}^{2}$Moment of Inertia $=m{\left(0\right)}^{2}+m{\left(l\sqrt{2}\right)}^{2}+m{\left(\dfrac{l}{\sqrt{2}}\right)}^{2}+m{\left(\dfrac{l}{\sqrt{2}}\right)}^{2}$$=3m{l}^{2}$