The escape velocity from a spherical planet A is 10 km/s. The escape velocity from another planet B whose density and radius are 10% of those of planet A, i $s______m/s.$
Options

Question

The escape velocity from a spherical planet A is 10 km/s. The escape velocity from another planet B whose density and radius are 10% of those of planet A, i s______m/s.

G1 Physics · Accepted Answer

Escape velocity from the surface of a planet is vₑ = √(2GM/R). For a spherical planet, M = (4/3)πR³ρ. Hence, vₑ = √[(8/3)πGρR²]. Therefore, vₑ ∝ R√ρ. For planet B, R(B) = 0.1R(A), ρ(B) = 0.1ρ(A). Thus, vₑ(B)/vₑ(A) = [R(B)/R(A)]√[ρ(B)/ρ(A)] = 0.1√0.1 = 1/(10√10). Given, vₑ(A) = 10 km/s = 10⁴ m/s. Therefore, vₑ(B) = 10⁴/(10√10) = 1000/√10 = 100√10 m/s. Correct option: C.