Question 61 of 280

Four identical solid spheres each of mass $m$ and radius $a$ are placed with their centres on the four corners of a square of side $b$. The moment of inertia of the system about one side of square where the axis of rotation is parallel to the plane of the square is :

A$\dfrac{8}{5}m{a}^{2}+m{b}^{2}$B$\dfrac{4}{5}m{a}^{2}+2m{b}^{2}$C$\dfrac{8}{5}m{a}^{2}+2m{b}^{2}$D$\dfrac{4}{5}m{a}^{2}$

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Answer: (C) $\dfrac{8}{5}m{a}^{2}+2m{b}^{2}$

$I=2\times \left(\dfrac{2}{5}m{a}^{2}\right)+2\times \left(\dfrac{2}{5}m{a}^{2}+m{b}^{2}\right)$
$I=\dfrac{8}{5}m{a}^{2}+2m{b}^{2}$