there are two planets.the ratio of radius of the two planets is k but ratio of acceleration due to gravity of both the planets is g.What will be the ratio of their escape velocity?

let one planet be a & other b then

R_a/Rb = K    ........1  (given)

g(acc due to gravity)= GM/R²

g_a/g_b = (M_a/M_b)*(R_b/R_a)² = 1         (given)

M_a/M_b = (R_a/R_b)² = K²       ..............2              (from eq 1)

now escape velocity = (GM/R)^1/2

 V_a/V_b = [(M_a/M_b)(R_b/R_a)]^1/2

         =[ k²(1/k)]^1/2                    (from eq 1 & 2)

         =k^1/2

thus the ratio of escape velocity is K^1/2

Approved

 approve my ans if u like