Question

Four particles each of mass m are placed at the comers of a square of side length$\ell$ The radius of gyration of the system about an axis perpendicular to the sauare and passing through centre is :

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

Answer 1

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

$\begin{array}{c}\text{Moment of Inertia (I) totat}\\ I=4\times m{\left(\frac{e}{\sqrt{2}}\right)}^2=2m{l}^2\text{(fowr masses)}\\ \text{let the radius of gyration be}k\\ \Rightarrow 4m\cdot k^2=2m{l}^2\\ \Rightarrow k=\frac{l}{\sqrt{2}}\\ \text{Hence, option}\left(A\right)\text{is correct.}\end{array}$