The centre of gravity of a ring is at its geometric centre, but how does it act on a pont where there is no material???
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Centre of gravity of the circle lies at its geometric center because the resultant weight of the circle acts at its center. A ring has a geometrical center at the point from which all the points on the surface of the ring is equidistant (center). As ring has a hollow circular opening beneath it's circumferential surface, the center of gravity or the center of mass lies outside it's physical body.
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