The escape velocity of a body on a planet A is 12km s ^ - 1 . The...

We know that escape velocity is given by,

$v = \sqrt{\dfrac{2GM}{R}} ⇒ \dfrac{{v}_{A}}{{v}_{B}} = \sqrt{\dfrac{{M}_{A}}{{M}_{B}} \times \dfrac{{R}_{B}}{{R}_{A}}} = \sqrt{\dfrac{{ρ}_{A}{{R}_{A}}^{3}}{{ρ}_{B}{{R}_{B}}^{3}} \times \dfrac{{R}_{B}}{{R}_{A}}} = \sqrt{\dfrac{{ρ}_{A}{{R}_{A}}^{2}}{{ρ}_{B}{{R}_{B}}^{2}}} = \sqrt{\dfrac{1}{4} \times \dfrac{4}{1}} ⇒ {v}_{B} = {v}_{A} = 12km{s}^{- 1}$