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Two massive stars of same mass M but different radii 1.5 R and 2R are separated by a distance d = 4R. A small body of mass M1000 is to be escaped from the mutual gravitational field of two stars, from the common centre of mass. The speed imparted to the body is n.GMR. Find ‘n’.

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answer is 2.

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Detailed Solution

After escaping, body will reach to infinity with zero final velocity.Both stars have same mass, therefore COM is located at mid-point.Ki+Ui=Kf+Uf⇒12mv2+−GMm2R−GMm2R=0 by solving v=2GMR,∴n=2

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Two massive stars of same mass M but different radii 1.5 R and 2R are separated by a distance d = 4R. A small body of mass M1000 is to be escaped from the mutual gravitational field of two stars, from the common centre of mass. The speed imparted to the body is n.GMR. Find ‘n’.