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 r₀ with time period T₀ around the mass M. Then, the particle is subjected to an additional central force, corresponding to the potential energy V_c(r)=m α/r³, where α 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 r₀ in the combined gravitational potential due to M and V_c(r), but with a new time period T₁, then (T₁²-T₀²)/T₁² is given by [ G is the gravitational constant.] [JEE Adv 2024 P2]

Question

Examsnet · Accepted Answer

Correct Answer is : 3αGMr02\; 3 α/G M r₀²GMr02​3α​

JEE Advanced 2024 Paper 2