The radii of planets A and B are R and 4R, and their densities are ρ and ρ/3 respectively. The ratio g(A): g(B) at their surfaces is:
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The radii of planets A and B are R and 4R, and their densities are ρ and ρ/3 respectively. The ratio g(A):g(B) at their surfaces is:

G1 Physics · Accepted Answer

For a spherical planet, g = GM/R² = (4πG/3)ρR, so g ∝ ρR. g(A)/g(B) = [ρR]/[(ρ/3)(4R)] = 3/4. Therefore g(A):g(B) = 3:4.