Final answer:
The answer explores the concept of gravitational potential along the axis of a ring with non-uniform mass distribution, indicating that the potential would depend on the distance from the center along the axis and the mass distribution.
Step-by-step explanation:
The student's question concerns the variation of gravitational potential due to a non-uniformly distributed mass around a ring with radius r, at a point along the axis passing through the center of the ring. In physics, the gravitational potential at a point in space is the potential energy per unit mass at that point due to a gravitational field. The calculation of gravitational potential in such a configuration involves integrating the contributions of each infinitesimal mass element of the ring, considering the symmetry and distribution of the mass.
The non-uniform distribution complicates the expression for gravitational potential, as one must take into account how mass is distributed with respect to r. Nonetheless, due to the symmetry around the axis, the potential would depend on the distance from the center along the axis (z-axis if the ring is in the yz-plane) and the overall mass distribution. It's important to note that the variation of potential would be smooth, and at large distances compared to the radius of the ring, it would approach the potential of a point mass.