First slide

Radius of Gyration

Question

The radius of gyration of a uniform rod of length L about an axis passing through its centre of mass is

Moderate

A

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

$\frac{L^{2}}{12}$
C

$\frac{L}{\sqrt{3}}$
D

$\frac{L}{\sqrt{2}}$

Solution

For uniform rod, the moment of inertia about an axis passing through its centre is $m L^{2} / 12$
$∴$ Radius of gyration, $K = \sqrt{\frac{I}{m}} = \sqrt{\frac{(m L^{2} / 12)}{m}} = \frac{L}{2 \sqrt{3}}$

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