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JEE Advanced2024PhysicsGravitationActual

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 / r^3 , where is a positive constant of suitable dimensions and r is the distance from the center of the orbit. If

Options

  1. A3 G M r₀^2
  2. B2 G M r₀^2
  3. CG M r₀^2
  4. D2 G M r₀^2

Correct answer

A. 3 G M r₀^2

Step-by-step solution

aligned & F ₁= GMm r ₀^2 & ~F ₂= GMm r ₀^2 - 3 ~m r ₀^4 & ₁^2 ₀^2 = F ₂ ~F ₁ = GM r ₀^2 - 3 r ₀^4 GM r ₀^2 & T ₀^2 ~T ₁^2 =1- 3 GMr ₀^2 & T ₁^2- T ₀^2 ~T ₁^2 = 3 GMr ₀^2 aligned

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