Question

the ratio between masses of two planets is 2:3 and the ratio between their radii is 3:2 then ratio between acceleration due to gravity on these two planets is

Answer 1

acceleration due to gravity on the first planet

g1=GM1/R1^2

acceleration due to gravity on the first planet

g2=GM2/R2^2

g1/g2= M1/M2* R2^2/R1^2

=2/3*(2/3)^2

=8/27

Answer 2

Acc to law of gravitation : mg1=GM1m/R1^2

g1= GM1 / R1^2

( considering that for the first planet variables are placed with 1 and for the second with 2 )

Similarly g2 = G M2/R2^2

As we know that M2 is twice of M1 and R2 is twice of R1

So g2= G2M1/(2R1)^2

g1/g2 = G M1/R1^2 X 4R1^2/G2M1

g1:g2 = 4:2 = 2:1