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 \alpha \/ r^3, where \alpha 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.] [JEE Adv 2024 P2]

Gravitation

Section: Physics

Question : 3 of 21

Marks: +1, -0

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 Vc(r)=mα∕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 Vc(r), but with a new time period T1, then (T12−T02)∕T12 is given by
[ G is the gravitational constant.]

[JEE Adv 2024 P2]

‌
3α
GMr02
‌
α
2GMr02
‌
α
GMr02
‌
2α
GMr02

Validate

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