Question

Four particles, each of mass $m$, are placed at the corners of a square of side length $l$. The radius of gyration of the system about an axis perpendicular to the square and passing through its center is

• A. $l$
• B. $\frac{l}{\sqrt{2}}$
• C. $l\sqrt{2}$
• D. $\frac{l}{2}$

Answer 1

The correct option is B $\frac{l}{\sqrt{2}}$


$I_x=m{\left(\frac{l}{\sqrt{2}}\right)}^2\times 4$
$I_x=2m{l}^2=4m{k}^2$
$k=\frac{l}{\sqrt{2}}$
Final Answer: $\left(a\right)$