Consider a planet whose density is same as that of the earth but whose radius is three times the radius ' R ' of the earth. The acceleration due to gravity ' g n ' on the surface

Question

Consider a planet whose density is same as that of the earth but whose radius is three times the radius ' R ' of the earth. The acceleration due to gravity ' g n ​ ' on the surface of planet is g n ​ = x . g where g is acceleration due to gravity on surface, of earth. The value of ' x ' is

TestHub · Accepted Answer

∴ ∴ ​ As , g = R 2 GM ​ and M = ρ V g = R 2 G ρ V ​ = R 2 G ρ 3 4 ​ π R 3 ​ g ∝ R ​ For the planet: Radius R = 3 R ∴ ∴ ∴ ​ g planet ​ = ( 3 R ) 2 G V planet ​ ​ where V planet ​ = 3 4 ​ π ( 3 R ) 3 g planet ​ = ( 3 R ) 2 G ρ 3 4 ​ π ( 3 R ) 3 ​ g planet ​ ∝ 3 R ​ ∴ g planet ​ g ​ = 3 R R ​ ....(since ρ is constant) ∴ ∴ ​ g planet ​ = 3 g x = 3 ​

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