Question

The radius of gyration of a uniform rod of length $L$, about an axis passing through its centre of mass and perpendicular to it's length is:

• A. $\frac{L}{2\sqrt{3}}$
• B. $\frac{L^2}{12}$
• C. $\frac{L}{\sqrt{3}}$
• D. $\frac{L}{\sqrt{2}}$

Answer 1

The correct option is A $\frac{L}{2\sqrt{3}}$

For a rod the $\text{MOI}$ about an axis passing through its centre of mass and $\perp$ to its plane is;
$I=\frac{m{L}^2}{12}....\left(i\right)$
Let the radius of gyration about the same axis is $k$,
$I=m{k}^2...\left(ii\right)$
From both equations:
$\frac{m{L}^2}{12}=m{k}^2$
$\Rightarrow k=\sqrt{\frac{L^2}{12}}$
$\therefore k=\frac{L}{2\sqrt{3}}$