The radii of two planets 'A' and 'B' are 'R' and '4R' 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:

Solution

Physics sir · 3 steps

Write the mass as density times volume, and g turns out to be proportional to ρ R alone.

1. Mass from density. The mass of a uniform planet is M = ρ × 4/3π R³. Put this into g = GM/R².

   g = G/R²·4/3π R³ ρ = 4/3π G ρ R

2. Take the ratio. Everything except ρ R is the same for both planets, so g_A/g_B = (ρ × R)/(ρ/3 × 4R) = 1/(4/3) = 3/4.
3. So. g_A : g_B = 3 : 4, which is option (d).

The idea to keep. When densities are given instead of masses, use g = 4/3π Gρ R. Surface gravity grows with radius, not against it, at fixed density.

Answer from the NTA final answer key. Solution by PrepWiser.