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A particle of mass m is under the influence of the gravitational field of a body of mass M (>> m). The particle is moving in a circular orbit of radius r 0 with time period T 0 around the mass M. Then, the particle is subjected to an additional central force, corresponding to the potential energy V c (r) = m /r 3 , where is a positive constant of suitable dimensions and r is the distance from the center of the orbit. If the particle moves in the same circular orbit of radius r 0 in the combined gravitational potential due to M and V c (r), but with a new time period T 1 , then (T 1 2 – T 0 2 )/ T 1 2 is given by [G is the gravitational constant.]
- 2 0 GMr 3
- 2 0 GMr 2
- 2 0 GMr
- 2 0 GMr 2
Correct answer: 2 0 GMr 3
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