Two rings having masses M and 2M, respectively, having the same radius are placed coaxially as shown in the figure. If the mass distribution on both the rings is non-uniform, then the gravitational potential at point P is

 

As all the points on the periphery of either ring are at the same distance from point P, the potential at point P due to the whole ring can be calculated as $\mathrm{V}=-\frac{\mathrm{GM}}{\sqrt{{\mathrm{R}}^2+{\mathrm{x}}^2}},$ where x is the axial distance from the centre of the ring. This expression is independent of the fact whether the distribution of mass is uniform or non-uniform
So, at  P,

$\mathrm{V}=-\frac{\mathrm{GM}}{\mathrm{R}\sqrt{2}}-\frac{\mathrm{G}\left(2\mathrm{M}\right)}{\mathrm{R}\sqrt{5}}$

$\mathrm{V}=-\frac{\mathrm{GM}}{\mathrm{R}}\left[\frac{1}{\sqrt{2}}+\frac{2}{\sqrt{5}}\right]$