Four particles each of mass ‘m’ are placed at the corners of a light square frame of side length ‘ l ‘. The radius of gyration of the system about an axis perpendicular to the plane of square and passing through its centre is

Four particles each of mass ‘m’ are placed at the corners of a light square frame of side length ' l '. The radius of gyration of the system about an axis perpendicular to the plane of square and passing through its centre is

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

Solution:

$I = \sum {mr}^{2} = 4 m {[\frac{l}{\sqrt{2}}]}^{2} = \frac{4 {ml}^{2}}{2} = 2 {ml}^{2}$
Radius of gyration $k = \sqrt{\frac{I}{M}} = \sqrt{\frac{2 {ml}^{2}}{4 m}} = \frac{l}{\sqrt{2}}$

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