Two planets A and B have radii R and 1.5R and densities ρ and ρ/2 respectively. The ratio of acceleration due to gravity at the surface of B to that at A is:
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Question

Two planets A and B have radii R and 1.5R and densities ρ and ρ/2 respectively. The ratio of acceleration due to gravity at the surface of B to that at A is:

G1 Physics · Accepted Answer

For a spherical planet, g = GM/R² and M = (4/3)πR³ρ Therefore, g = (4/3)πGρR So, gʙ/gₐ = [(ρ/2)(1.5R)]/(ρR) = 1.5/2 = 3 4 \frac{3}{4} 4 3 ​ Hence, gʙ : gₐ = 3 : 4 Therefore option D follows.