Gravitation on Rigid Body

Classical Mechanics Level pending

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 $$k$$.

×