Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface o

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Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g ′ , then

TestHub · Accepted Answer

The acceleration due to gravity on the new planet can be found using the relation g = R 2 GM ​ ... ( i ) but M = 3 4 ​ π R 3 ρ , ρ being density. Thus, Eq. (i) becomes ∴ g = R 2 G × 3 4 ​ π R 3 ρ ​ = G × 3 4 ​ π Rρ ⇒ ∴ ⇒ ⇒ ​ g ∝ R g g ′ ​ = R R ′ ​ g g ′ ​ = R 3 R ​ = 3 g ′ = 3 g ​

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