Gravitation on Rigid Body

A long spherical mass $M$ is fixed at one position and two identical point masses $m$ are kept on a line passing through the centre of $M$ . The point masses are connected by a rigid massless rod of length $l$ and this assembly is free to move along the line connecting them.

All three masses interact only through their mutual gravitational interaction. When the point mass nearer to $M$ is at distance $r = 3l$ from $M$ , then tension in rod is zero for $m = k \left( \frac M {288} \right)$ .

Find the value of $k$ .