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Question:

A body of mass m is moving in a circular orbit of radius R about a planet of mass M. At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius R/2, and the other mass, in a circular orbit of radius 3R/2. The difference between the final initial total energies is:

-GMm/2R

-GMm/6R

+GMm/6R

GMm/2R

Solution:

Initial energy = -GMm/R + 1/2 GMm/R = -GMm/2R
Final energy = -GMm/(2(R/2)) - GMm/(2(3R/2))
ΔE = -GMm/6R