A large spherical mass \( M \) is fixed at one position and two identical point masses \( m \) a...

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A large spherical mass \( M \) is fixed at one position and two identical point masses \( m \) are kept on a line passing through the center 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 \( r=3 l \) from \( M \), the tension in the rod is zero for \( m=k(M / 288) \). The value of \( k \) is
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