Let the mass and radius of the circular disk and circular ring are M and R.
We know
Radius of gyration is given by (K)
K=√IM
∴ Radius of gyration of disk Kdisc=√IdiscM ...(i)
Radius of gyration of ring, Kring=√IringM ....(ii)
Dividing equation (i) and (ii)
KdiscKring=√IdiscIring=
⎷MR22MR2=1√2
where Idisc and Iring are the moment of inertia of the circular disk and circular ring about their natural axis.