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The radius of a planet is twice the radius of earth. Both have almost

The radius of a planet is twice the radius of earth. Both have almost equal average mass densities. If Vp and Ve are escape velocities of the planet and the earth, respectively, then,

Options

(a) Ve = 1.5 Vp
(b) Vp = 1.5 Ve
(c) Vp = 2 Ve
(d) Ve = 3 Vp

Correct Answer:

Vp = 2 Ve

Explanation:

Escape velocity, vₑ = R√(8/3 πGP)
⇒ vₑ ∞ R ⇒ Vₚ / Vₑ = Rₚ / Rₑ = 2
Vₚ = 2 vₑ

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