The escape velocity from the Earth is 11.2 k m s - 1 . The escape velocity from a planet having twice the radius and the same mean density is ( in km s - 1 )

Step-by-step solution

Escape velocity from the Earth, ( v e ) = 11.2 k m s - 1 Let the mass, radius and density of Earth be M , R and ρ , respectively, and for the given planet, mass, radius and density are M ′ , R ′ and ρ ' , respectively. ∴ Escape velocity from the Earth, v e = 2 G × 4 3 π R 3 ρ R v e = 8 G π R 2 ρ 3 … . i Similarly, escape velocity from the given planet, v ′ e = 8 G π R ′ 2 ρ 3 … . i i Dividing Eq. ( i ) by Eq. ( ii ), we get, v e v ′ e = 8 G π R 2 ρ 3 × 3 8 G π R ′ 2 ρ = R 2 4R ′ 2 or 11.2 v ′ e = R 2 R ∴ v ′ e = 22