Question

Four particles each of mass ${}^{\prime }{m}^{\prime }$ are placed at the corners of a square of side ${}^{\prime }{L}^{\prime \prime }$. The radius of gyration of the system about an axis normal to the square and passing through its centre.

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

Answer 1

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

I=m$(\frac{l}{\sqrt{2}}{)}^2\times 4=2m{l}^2$

$2m{l}^2=4m{r}^2$

Radius of gyration r=$\frac{l}{\sqrt{2}}$