Two planets P₁ and P₂ with equal mass have radii R₁ and R₂ , respectively, where R₂= R₁ 2 . The escape speeds of P₁ and P₂ are v₁ and v₂ , respectively. Then v₂ v₁ is :

Step-by-step solution

The escape speed of a planet of mass M and radius R is given by v = 2GM R . For planet P₁ , the escape speed is v₁ = 2GM R₁ . For planet P₂ , the escape speed is v₂ = 2GM R₂ . Taking the ratio of the escape speeds: v₂ v₁ = R₁ R₂ Given that R₂ = R₁ 2 , substituting this into the equation gives: v₂ v₁ = R₁ R₁ 2 = 2 Answer: 2