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

1. A

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

2. B

$\frac{\mathrm{l}}{2}$

3. C

l

4. D

$\sqrt{2}\mathrm{l}$

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### Solution:

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

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