The acceleration due to gravity on moon is 6 1 th times the acceleration due to gravity on earth. If the ratio of the density of earth ' e e ' to the density of moon ' e m '

Question

The acceleration due to gravity on moon is 6 1 th ​ times the acceleration due to gravity on earth. If the ratio of the density of earth ' e e ​ ' to the density of moon ' e m ​ ' is 3 5 ​ then the radius of moon ' R m ​ ' in terms of the radius of earth ' R e ​ ' is

TestHub · Accepted Answer

We know g = R 2 GM ​ And the relation between mass and density of the planet is given by ​ M = ρ ( 3 4 ​ π R 3 ) ∴ g = ( 3 4 π G ​ ) ρR = K ρR ​ Given, g m ​ = 6 1 ​ g e ​ and e m ​ = 5 3 ​ e e ​ ​ ⇒ g e ​ g m ​ ​ = e e ​ R e ​ e m ​ R m ​ ​ = 6 1 ​ ⇒ 5 R e ​ 3 R m ​ ​ = 6 1 ​ ⇒ R m ​ = 18 5 ​ R e ​ ​

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