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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 and initial total energies is:

1. -GMm/2R
2. +GMm/6R
3. -GMm/6R
4. GMm/2R

Correct answer: -GMm/6R

Solution

The total energy of an object in a circular orbit is given by the formula E = -GMm/(2R). When the body splits into two equal masses, their new orbits have different radii, which affects their individual energies. The change in total energy is calculated by finding the difference between the initial energy and the sum of the energies of the two new orbits, resulting in a net decrease of -GMm/6R.

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