Gravitation 5 Question 10

11. A large spherical mass M is fixed at one position and two identical 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=kM288. The value of k is

(2015 Adv.)

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Answer:

Correct Answer: 11. (7)

Solution:

  1. For point mass at distance r=3l

GMm(3l)2Gm2l2=ma

For point mass at distance r=4l

GMm(4l)2+Gm2l2=ma

Equating the two equations, we have

GMm9l2Gm2l2=GMm16l2+Gm2l2

7GMm144=2Gm2l2m=7M288



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