Two spherical planets A and B are made of the same uniform material of density ρ. Planet A has radius 2R while planet B has radius R.
(i) Express the mass of each planet in terms of ρ and its radius.
(ii) Using your results from part (i), obtain the ratio of the minimum speeds required to escape from the surfaces of planets A and B.
(iii) Compute the numerical value of this ratio.