Radius of Gyration of a body about an axis is the effective distance from the axis where the whole mass can be assumed to be concentrated so that moment of inertia remains the same.

- wherein

$I= MK^{2}$

$K= \sqrt{\frac{I}{M}}$

MI of system w.r.t  an axis perpendicular to plane and passing through  one centre

$= \frac{ml^2}{3}+ \frac{ml^2}{3} + \left [ \frac{ml^2}{12}+m\left [ \frac{\sqrt3l}{2} \right ] ^2 \right ] \\\\ = \frac{2ml^2}{3}+\frac{10ml^2}{12} = \frac{18}{12}ml^2$

$NOW \\\\ 3mk^2 = \frac{3}{2}ml^2\\\\k=l/\sqrt2$

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