The ratio of escape velocity at earth υ e to the escape velocity at a planet υ p whose radius and mean density are twice as that of earth is:

Step-by-step solution

v e v P = 2 G M e R e 2 G M P R P = M e R P M P R e = ρ e 4 3   π R e 3 R P ρ p 4 3   π R P 3 R e v e v P = ρ e R e 2 ρ p R P 2 = 1 2 × 2 2 = 1 2 2