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 λ 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 λ from M, the tension in the rod is zero for m = k 
. The value of k is
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(7)
Sol. For point mass at distance r = 3 λ
– 
= ma
For point mass at distance r = 4 λ
+ 
= ma
– 
= 
+ 
= 
m = 
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