A square frame is made of four identical rods each of length 1m and mass 0.5 kg. Then radius of gyration of the system about one of its side is 

moment of inertia of a square about its one side is 

$$\begin{gathered} \frac{m{l}^2}{3}+\frac{m{l}^2}{3}+m{l}^2=4m{k}^2 where k is the radius of gyration and 4m is the total mass \\ \frac{5m{l}^2}{3}=4m{k}^2 \\ k=\sqrt{\frac{5}{12}}l \end{gathered}$$