JEE Advanced 2024 Physics question
A particle of mass is under the influence of the gravitational field of a body of mass . The particle is moving in a circular orbit of radius with time period around the mass . Then, the particle is subjected to an additional central force, corresponding to the potential energy , where is a positive constant of suitable dimensions and is the distance from the center of the orbit. If the particle moves in the same circular orbit of radius in the combined gravitational potential due to and , but with a new time period , then is given by [ is the gravitational constant.]
Solution
Initially . The additional force is , i.e. directed outward (repulsive). In the same orbit: . Dividing by the first equation: $ =
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