Solve the following :


The radius of gyration of a uniform disc about a line perpendicular to the disc equals its radius. Find the distance of the line from the centre.


$I_{a x i s}=I_{C O M}+m d^{2}$

$m k^{2}=\frac{m r^{2}}{2}+m d^{2}$

$\Rightarrow m r^{2}=\frac{m r^{2}}{2}+m d^{2}$

$\Rightarrow d=\sqrt{2}$

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