The ratio of radius of gyration of a circular disc about a tangential axis in the plane of the disc - Physics - System of particles and rotational motion

Question

The ratio of radius of gyration of a circular disc about a
tangential axis in the plane of the disc and a circular ring of the
same radius about a tangential axis in the plane of the ring is

Neha Gupta · Accepted Answer

DiscMoment of inertia about the diameter = Id = mr24moment of inertia about the tangential axis I = Id+mr2Idisc = mr24+mr2 = 5mr24Kdisc = radius of gyration5mr24 = mkdisc2kdisc = 54rRingMoment of inertia about the diameter = Id ring = mr22moment of inertia about the tangential axis I = Id ring+mr2Iring = mr22+mr2 = 3mr22kring  = radius of gyration of ringmkring2 = 3mr22kring  = 32 rkdisckring = 54r32 r = 56

The ratio of radius of gyration of a circular disc about a tangential axis in the plane of the disc and a circular ring of the same radius about a tangential axis in the plane of the ring is