The problem of attraction of an infinitesimal particle by the gravitational force induced by a massive body composed of a ring (in the form of a circle) of radius a and a punctual body at the center of the ring is considered. We study the singularity problem of the solutions associated with this problem, and we prove that all the singularities are due to collision. In the planar equatorial case (the plane that contains the ring) we are able to prove that the reciprocal is true. Moreover, we observe that zero angular momentum is a necessary condition in order to have solutions that go or start in collision with the central body or with the ring. Still in the planar case, we give all the possible global phase portraits as a function of the angular momentum. More precisely, we show that inside the ring there are topologically four possible phase portraits according to the variation of the angular momentum, while outside the ring there are topologically five possible phase portraits according to the variation of the angular momentum.