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Two particles of mass m and M are initially at rest and infinitely separated from each other. Due to mutual interaction they approach each other. Their relative velocity of approach at a separation distance d between them is

a
2GdM+m
b
2G(M+m)d
c
2G(M−m)d
d
2GdM+m

detailed solution

Correct option is B

Here we assume that one mass is at rest and the other mass equal to reduced mass μ[μ=Mm/(M+m)] is in motion. Using conservation of energy, the final energy is12μv2−GMmd0or V2=2GMmμd=2GMm(M+m)mMd=2G(M+m)dV=2G(M+m)d

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