Q. 135.0( 1 Vote )

Find the radius of gyration of a circular ring of radius r about a line perpendicular to the plane of the ring and passing through one of its particles.

Answer :

We need to determine the moment of inertia perpendicular to the ring, passing though it's center.



First let’s take a point on the rim, this point is perpendicular to the ring and moment of Inertia will be-




If the ring passes through its particles at a distance of r, it will be parallel to the axis.


By applying parallel axis theorem



Now for a new line, radius of gyration will be a, therefore



Equating both sides of equation for I’-




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