The ratio of escape velocity on earth (νe ) to the escape velocity on a planet (νp) whose radius and mean density are twice as that of earth is [NEET 2016]

Since, the escape velocity of the earth can be given asve=2gR=2GMR2R=R83πGρ                                        ∵ mass of earth, m=ρ43πR3⇒  ve=R83πGρ                                     … (i)As it is given that, the radius and mean density of planet are twice as that of the earth. So, escape velocity at planet will bevp=2R83πG2p                                      …(ii)On dividing Eq. (i) by Eq. (ii), we getvevp=R83πGρ2R83πG2ρ⇒vevp=122