Question

two planets of radii r1 and r2 are made of same material . the ratio of acceleration due to gravity g1/g2 at the surface of the planets is:

Answer 1

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 

Answer 2

Answer is r1/r2

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