The escape velocities of two planets A and B are in the ratio 1: 2. If the ratio of their radii respectively is 1: 3, then the ratio of acceleration due to gravity of planet A to the acceleration of gravity of planet B will be :

Solution

Physics sir · 3 steps

Write g in terms of escape velocity and radius, then take the ratio. The mass of the planet cancels out.

1. Link v and g. Escape velocity is vₑ = √(2GM/R). Since g = GM/R², we have GM = gR², so vₑ = √2gR.

   vₑ² = 2gR ⇒ g = vₑ²/2R

2. Take the ratio. g_A/g_B = (v_A/v_B)² × R_B/R_A = (1/2)² × 3/1.
3. So. g_A/g_B = 1/4 × 3 = 3/4, which is option (c).

The idea to keep. Remember vₑ = √2gR. It lets you swap between escape velocity and surface gravity without ever needing the planet's mass.

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