Question

if the ratio of a body of mass m measured on two different planets A and B is 1:2 and the ratio of the radii of two planets A and B is 2:4 respectively, then the ratio of the masses of two planets is respectively

Answer 1

Answer:

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: Ratio of mass on A : Ratio of mass on B = 1:8

Explanation: