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Gravitation · Question 2

JEE Advanced 2025 Paper 2MCQHard📈 Topic in 33% papers+4−1
1

Consider a star of mass m2 kg revolving in a circular orbit around another star of mass m1 kg with m1 m2. The heavier star slowly acquires mass from the lighter star at a constant rate of kg/s. In this transfer process, there is no other loss of mass. If the separation between the centers of the stars is r, then its relative rate of change 1r drdt (in s-1) is given by:

  1. - 3 2m2
  2. - 2 m2
  3. - 2 m1
  4. - 3 2m1

Answer

(2) - 2 m2

Solution

Mass transfer is internal, so orbital angular momentum is conserved: L=m2 Gm1r (for m1 m2).

L= m2+ 12 m1+ 12 r=const

m2m2+ 12 m1m1+ 12 rr=0, with m2=- , m1=+

1r drdt= 2 m2- m1 + 2 m2 (since m1 m2)

The magnitude matches (B), but the separation actually increases (positive sign), so no option is exactly correct; the official key awarded marks to all.

Answer: (B) in magnitude (official: marks to all)

JEE Advanced 2025 Paper 2

Keep practising — Gravitation

2

A geostationary satellite above the equator is orbiting around the earth at a fixed distance r1 from the center of the earth. A second satellite is orbiting in the equatorial plane in the opposite direction to the earth's rotation, at a distance r2 from the center of the earth, such that r1=1.21 r2. The time period of the second satellite as measured from the geostationary satellite is 24p hours. The value of p is

JEE Advanced 2025 Paper 2
3

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) = m /r3, 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 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.]

  1. 3 GMr02
  2. 2GMr02
  3. GMr02
  4. 2 GMr02
JEE Advanced 2024 Paper 2

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