Question
Show that radius of gyration of ring about an axis passing through centre and perpendicular to the plane of ring is equal to radius of ring.
Solution
The moment of inertia of ring about an axis passing through centre and perpendicular to the plane of ring is,
I=MR2 ...(1)
If K is radius of gyration then
I =MK2 ...(2)
From (1) and (2),
K=R
Hence, the radius of gyration of ring about an axis passing through the centre and perpendicular to the plane of ring is equal to the radius of ring.
