The center of mass of a uniform ring lies at its geometrical center i.e. outside the body. But we generally define center of mass as a point in which if we apply a force, the whole body will move in the same way as if the whole of the mass is assumed to be concentrated there and how that point mass moves under that force. So my question is how can we apply a force to a point not on body (here the point is the center of mass) and still see the force's effect on that body?
For example consider this: suppose a uniform ring hanging in mid air in a gravity free environment in $y$-$z$ plane. Now you have to move the ring along x-axis so that whole ring remains in a plain. No torque is to be applied and you can not put any charge on the ring and distribute it uniformly and apply an electric field along $x$-axis. How can we do it?