The radii of planets A and B are R and 4R, and their densities are ρ and ρ/3 respectively. The ratio $\frac{g_{A}}{g_{B}}$ 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 \frac{g_{A}}{g_{B}} g B ​ g A ​ ​ 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 \frac{3}{4} 4 3 ​ . Therefore g(A):g(B) = 3:4.

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 \frac{g_{A}}{g_{B}} g B ​ g A ​ ​ at their surfaces is:

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 \frac{g_{A}}{g_{B}} g B g A at their surfaces is: