Question

Find the radius of gyration of a thin uniform rod of mass ${}^{\prime }{m}^{\prime }$ and length $l=9\text{m}$ about an axis passing through one end and perpendicular to the rod as shown in figure.

• A. $\sqrt{3}\text{m}$
• B. $2\sqrt{3}\text{m}$
• C. $\frac{\sqrt{3}}{2}\text{m}$
• D. $3\sqrt{3}\text{m}$

Answer 1

The correct option is D $3\sqrt{3}\text{m}$

Given, length of thin uniform rod $\left(l\right)=9\text{m}$
Moment of inertia of rod about ${}^{\prime }{\text{z}}^{\prime }$ axis $I_z=\frac{m{l}^2}{3}$
Radius of gyration of rod about ${}^{\prime }{\text{z}}^{\prime }$ -axis is given by:
$I_z=m{k}^2$
$\Rightarrow k=\sqrt{\frac{I_z}{m}}$
$\Rightarrow k=\sqrt{\frac{l^2}{3}}=\frac{l}{\sqrt{3}}=3\sqrt{3}\text{m}$