Question

$K$ is the radius of gyration of a thin rod when it is rotating about an axis perpendicular to the length of the rod and is passing through it's centre. The length of that rod is :

• A. $12K$
• B. $3K$
• C. $2\sqrt{3}K$
• D. $\sqrt{3}K$

Answer 1

Answer: (C)

$2\sqrt{3}K$

$I=\frac{M{L}^2}{12}=M{K}^2$

above equation is relevent because radius of gyration is equivalent distance from axis of rotation,finally;

$K=\frac{L}{\sqrt{12}}$
$L=2\sqrt{3}K$