First slide

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

A

$(\frac{\sqrt{2}}{3}) L$
B

$\frac{4 L}{3}$
C

$(\sqrt{\frac{2}{3}}) L$
D

$\frac{2 L}{3}$

Solution

M.I about Z axis
$\frac{{ml}^{2}}{3} + \frac{{ml}^{2}}{3} = {mK}^{2}$
$\frac{2 {ml}^{2}}{3} = 3 {mK}^{2}$
$k = \frac{\sqrt{2}}{3} l$

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