Why centre of gravity of ring is out of its body

There's no reason why the center of gravity must be in a place where
there is a any mass. 

The center of gravity is simply a LOCATION ... the place where the 
amount of mass in any direction from it is the same amount. 

For that matter, whenever you know the location of the center of gravity
for ANY object, you can always go in there and scoop our a tiny spherical
hole at that place.  Then the center of gravity won't move, but it will be in an
empty space, 'outside the body' of the object.

Here are a few more points to ponder:

-- The center of gravity of a basketball, beach ball, tennis ball, or any other
inflated ball is the center of the ball, where there is no part of the skin.

-- The center of gravity of a party balloon is somewhere inside the balloon,
where there is no rubber.  If the balloon is spherical, then its center of gravity
is the center of the sphere.

-- The center of gravity of a square is the center of the square, not on any
of its sides.

-- The center of gravity of a triangle is the centroid of the triangle, not on any
of its sides.