Four particles,each of mass m,are placed at t | vedclass

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(A) The distance of each particle from the center $P$ of the square is $r = \frac{l}{\sqrt{2}}$.The moment of inertia $I$ of the system about an axis

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$ \frac{l}{\sqrt{2}} $

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(A) The distance of each particle from the center $P$ of the square is $r = \frac{l}{\sqrt{2}}$.The moment of inertia $I$ of the system about an axis passing through the center $P$ and perpendicular to the plane is given by:$I = \sum m_i r_i^2 = 4 	imes m 	imes r^2 = 4m \left( \frac{l}{\sqrt{2}} ight)^2 = 4m \left( \frac{l^2}{2} ight) = 2ml^2$.The radius of gyration $K$ is defined by the relation $I = MK^2$,where $M$ is the total mass of the system.Here,$M = 4m$,so:$4mK^2 = 2ml^2$$K^2 = \frac{2ml^2}{4m} = \frac{l^2}{2}$$K = \frac{l}{\sqrt{2}}$.

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

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