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  4. The radius of gyration of a solid sphere of radius r about a certain axis is r. The distance of this axis from the centre of the sphere is

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Q. The radius of gyration of a solid sphere of radius $r$ about a certain axis is $r$. The distance of this axis from the centre of the sphere is

System of Particles and Rotational Motion

Solution:

$I =m k^{2}=m r^{2}=I_{ CM }+m h^{2}=\frac{2}{5} m r^{2}+m h^{2}$
or $ h^{2}=\frac{3}{5} r^{2}$ or $h=\sqrt{0.6} r$