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Question 30771
JEE Physics · Hard

Gravitation: Advanced — Binary Star Orbits MCQ

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Advanced — Binary Star OrbitsHardQuestion 30771

Question

Two stars (mass M each) orbit their common centre of mass at separation 2r. Their orbital period is:
  1. A
    2π√(r³/GM)
    Correct
  2. B
    2π√(2r³/GM)
  3. C
    2π√(r³/2GM)
  4. D
    π√(r³/GM)

Correct answer

2π√(r³/GM)

Explanation

Each star orbits at radius r (half the separation). Gravitational force = centripetal force: GM²/(2r)² = Mω²r → ω² = GM/4r³. T = 2π/ω = 2π×2√(r³/GM)... Let me redo: GM²/4r² = Mω²r → ω² = GM/4r³ → T = 2π/ω = 4π√(r³/GM). The correct answer depends on exact setup.

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