The ratio of radii of gyration of a circular ring and a circular disc, of the same mass and radius, about an axis passing through their centres and perpendicular to their planes are

Question

Infinity Learn · Accepted Answer

Let M and R be mass and radius of the ring and the disc respectively. Then, Moment of inertia of ring about an axis passing through its centre and perpendicular to its plane isIring $$=MR2Moment$$ of inertia of disc about the same axis $$isIdisc=MR22$$ As $$I=Mk2$$ where k is the radius of gyration ∴  Iring $$=Mkring$$ $$2=MR2$$  or   kring $$=R$$  and   Idisc $$=Mkdisc$$ $$2=MR22$$  or   kdisc $$=R2$$ ∴  kring kdisc $$=RR/2=21$$ kring :kdisc $$=2$$:$$1$$

The ratio of radii of gyration of a circular ring and a circular disc, of the same mass and radius, about an axis passing through their centres and perpendicular to their planes are

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