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NTA Abhyas JEE Main2020PhysicsGravitationPractice

Gravitational acceleration on the surface of a planet is 6 1 1 g , where g is the gravitational acceleration on the surface of the earth. The average mass density of the planet is 2 3 times that of the earth. If the escape speed on the surface of the earth is taken to be 11 kms -1 , the escape speed on the surface of the planet in kms -1 will be.

Correct answer

3

Step-by-step solution

g = GM R 2 = G 4 3 π R 3 ρ R 2 or g ∝ ρ R or R ∝ g ρ Now escape velocity, ν e ∝ 2 gR or ν e ∝ gR or ν e ∝ g × g ρ ∝ g 2 ρ ∴ ν e planet = 11 km s -1 6 1 2 1 × 3 2 = 3 km s -1

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