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Question 30777
JEE Physics · Hard

Gravitation: Advanced — Escape from Orbit MCQ

Solve this quality-checked JEE multiple-choice question, then review the correct answer and explanation.

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Advanced — Escape from OrbitHardQuestion 30777

Question

To escape Earth's gravity from a circular orbit at radius r (speed v₀ = √(GM/r)), the speed must be increased to:
  1. A
    √(2GM/r) = √2 v₀
    Correct
  2. B
    2v₀
  3. C
    v₀ + √(gR)
  4. D
    v₀/√2

Correct answer

√(2GM/r) = √2 v₀

Explanation

Escape speed from any point at radius r: v_e = √(2GM/r) = √2 × √(GM/r) = √2 × v_orbital. The spacecraft must increase speed by factor √2 (increase of about 41%).

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