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 2 R , and t

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 2 R ​ , and the other mass, in a circular orbit of radius 2 3 R ​ . The difference between the final and initial total energies is:

TestHub · Accepted Answer

Initial gravitational potential energy, E i ​ = − 2 R GM m ​ Final gravitational potential energy, E f ​ ​ = − 2 ( 2 R ​ ) GM m /2 ​ − 2 ( 2 3 R ​ ) GM m /2 ​ = − 2 R GM m ​ − 6 R GM m ​ = − 6 R 4 GM m ​ = − 3 R 2 GM m ​ ​ ∴ Difference between initial and final energy, E f ​ − E i ​ = R GM m ​ ( − 3 2 ​ + 2 1 ​ ) = − 6 R GM m ​

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