Four particles, each of mass M, move along a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is

A large 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 (see figure).  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 a distance $r=3l$  from  M , the tension in the rod is zero for  $m=k\left(\frac{M}{288}\right)$.  The value of  k is