The ratio of radii of planets A and B is K₁ and ratio of accelerations due to gravity on them is K₂. The ratio of escape velocities from them will be

Options

(a) K₁K₂
(b) √K₁K₂
(c) √K₁/K₂
(d) √K₂/K₁

Correct Answer:

√K₁K₂

Explanation:

Escape velocity Ve=(√2Rg)
The radii of two planets R₁/R₂=K₁
The acceleration due to gravity of two planets g₁/g₂=K₂
The escape velocity of two planets v₁/v₂=?
v₁/v₂=(√2R₁g₁/2R₂g₂)
=(√R₁/R₂.g₁/g₂)
=(√K₁K₂ )