Question

Find the radius of gyration of a thin uniform rod of mass $M$ and length $L=3\text{m}$ about an axis passing through one end and perpendicular to rod as shown in figure.

• A. $3m$
• B. $\sqrt{3}m$
• C. $\frac{1}{\sqrt{3}}m$
• D. $1m$

Answer 1

The correct option is B $\sqrt{3}m$


As we know,
Moment of inertia of a rod of mass $M$ about $I_z=\frac{M{L}^2}{3}$.

The radius of gyration of rod about about $I_z$ is given by $K=\sqrt{\frac{I}{M}}$
$K=\sqrt{\frac{\frac{M{L}^2}{3}}{M}}=\sqrt{\frac{1}{3}}\times L$
$=\frac{1}{\sqrt{3}}\times 3\text{m}$

$=\sqrt{3}\text{m}$