Question

Two planets have the same average density but their radii are r and R. If acceleration due to gravity on these planets be g and G respectively, then
what is the ratio of g /G​

Answer 1

Answer:

F G mm/r2

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Answer 2

Answer:

due to gravity can be described as g = GM/R^2 Mass of the planets: M1 = density*volume ... due to gravity on these planets be g1 and g2 respectively then ... Now the ratio of acceleration due to gravity

We know that the acceleration due to gravity can be described as 

g = GM/R^2 

Mass of the planets: M1 = density*volume = d*(4/3*pi*r1^3) 

M2 = d*(4/3*pi*r2^3) 

Now, g1 = 4(G*d*pi*r1^3)/(3r1^2) = 4/3*G*d*r1 

And g2 = 4(G*d*pi*r2^3)/(3r2^2) = 4/3*G*d*r2 

Now the ratio of acceleration due to gravity 

We get, g1/g2 = 4/3*G*d*r1/4/3*G*d*r2 = r1/r2 

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