The radii of two planets A and B are R and 4 R and their densities are ρ and ρ 3 respectively. The ratio of acceleration due to gravity at their surfaces g A : g B will be

Step-by-step solution

Acceleration due to gravity is written as g = G M r 2 = G × 4 3 × π × r 3 × ρ r 2 = 4 π G 3 ρ r   Given: r A = R r B = 4 R ρ A = ρ ρ B = ρ 3 Hence, the ratio is g A g B = R × ρ 4 R × ρ 3 = 3 4 .