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JEE MainPhysicsGravitation

A satellite is orbiting a planet of radius R at an altitude R above its surface with an orbital speed v₀ . The escape velocity from the surface of the planet in terms of v₀ will be :

Options

  1. A2 v₀
  2. B4v₀
  3. C2v₀
  4. Dv₀ 2

Correct answer

C. 2v₀

Step-by-step solution

The orbital radius of the satellite is the distance from the center of the planet. Since it is at an altitude R , the orbital radius is r = R + R = 2R . The orbital speed of the satellite is: v₀ = GM 2R The escape velocity from the surface of the planet is: v_e = 2GM R Taking the ratio of v_e to v₀ : v_e v₀ = 2GM R GM 2R = 2GM R 2R GM = 4 = 2 Thus, v_e = 2v₀ . Answer: 2v₀

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