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 \(k\).

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