Two rings having masses $\mathrm{M}$ and $2\mathrm{M}$ ,respectively, having same radius are placed coaxially as shown in figure.

If the mass distribution on both the rings is non-uniform, then gravitational potential at point $P$ is

As all the points on the periphery of either ring are at same distance from point $P$ , the potential at point $P$ due to whole ring can be calculated as $V=-\left(GM\right) /\left(\sqrt{R^2+x^2}\right)$ where $x$   is 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, $V$  at $P$ is $V=-\frac{GM}{\sqrt{2}R}-\frac{G\times 2M}{\sqrt{5}R}$

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