Radius of Gyration

Question

Three thin rods each of length 'L' and mass M are placed along X, Y and Z axis such that one end of each rod is at origin. The radius of gyration of this system about Z–axis is

Easy

Solution

M.I about Z axis

$\frac{{\mathrm{ml}}^{2}}{3}+\frac{{\mathrm{ml}}^{2}}{3}={\mathrm{mK}}^{2}$

$\frac{2{\mathrm{ml}}^{2}}{3}=3{\mathrm{mK}}^{2}$

$\mathrm{k}=\frac{\sqrt{2}}{3}\mathrm{l}$

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