Question

Four point size bodies each of mass $m$ are fixed at four corners of a light square frame of side length $L$. The radius of gyration of these four bodies about an axis perpendicular to the plane of frame passing through its centre is:

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

Answer 1

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

$I=4\left(m{\left(\frac{L}{\sqrt{2}}\right)}^2\right)$
$=2m{L}^2$
So we have radius of gyration equivalence equation as,
$4m{k}^2=2m{L}^2$
$k=\frac{L}{\sqrt{2}}$