Question

Show that radius of gyration of disc about transverse axis through centre of mass is equal to radius of gyration of a ring about an axis coinciding with its diameter,if disc and ring have same radius.

Answer 1

moment of motion of disc about transverse axis is $I=\frac{M{R}^2}{2}$
So,radius of gyration $\left(k\right)=\sqrt{\frac{I}{M}}$
$K=\sqrt{\frac{M{R}^2}{2m}}=\frac{R}{2}$
moment of Inertia of ring about diameter
$I=\frac{M{R}^2}{2}$
radius of gyration $\left(K\right)=\sqrt{\frac{I}{M}}=\frac{R}{\sqrt{2}}$
so radius of gyration is same for the both cases having same mass