Question

Two sperical planets A and B have same mass but density inthe ratio is 8:1 for these planets the acceleration due to gravity on the surface A to B the ratio ....

Answer 1

Density = Mass/Volume
Let mass = m
density = 8x,x
Now volumes= m/8x, m/x
Volume = 4πr³/3
So radii = ∛3m/32π , ∛3m/4π
Acceleration due to gravity = GM/r²
So ratio = $M_{1} / r_{1}$ *$r_{2}/ M_{2}$
              But M1 = M2
           So , ratio = $r_{2}/r_{1}$
                          = ∛3m*32π/4π*3m
                          =∛8
                         Planet B to A = 2/1
Therefore, Ratio A:B = 1:2