Halliday, Resnick & Walker — Gravitation: Problem Problem_71

Several planets (Jupiter, Saturn, Uranus) are encircled by rings, perhaps composed of material that failed to form a satellite. In addition, many galaxies contain ring-like structures. Consider a homogeneous thin ring of mass \(M\) and outer radius \(R\) (Fig. 13.32). (a) What gravitational attraction does it exert on a particle of mass \(m\) located on the ring’s central axis a distance \(x\) from the ring center? (b) Suppose the particle falls from rest as a result of the attraction of the ring of matter. What is the speed with which it passes through the center of the ring?