Gravitational acceleration on the surface of a planet is 6 11 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

Question

Gravitational acceleration on the surface of a planet is 6 11 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 km/s, the escape speed on the surface of the planet in km/s will be

TestHub · Accepted Answer

g = G M R 2 = G R 2 4 3 π R 3 ρ = 4 3 π G R ρ i.e. g ∝ R ρ g P g E = 6 g E 11 g E = 6 11 and ρ E ρ P = 3 2 and g P g E = R P ρ P R E ρ E ∴ R P R E = g P ρ E g E ρ P = 6 11 × 3 2 ∴ Escape velocity v = 2 g R ∴ v P v E = g P g E × R P R E = 6 11 × 6 11 × 3 2 = 3 11 ∴ v P = 3 11 × v E = 3 11 × 11 = 3 km s - 1

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