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

Question

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.]

Quantrex Academy · Accepted Answer

Correct answer: A. 3 G M r_0^2

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

JEE Advanced Physics Question (2024) — Solution

Question

Options

Answer

Step-by-step solution