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.

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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