Question

two planets have masses in ratio 1:10 and radii in ratio 2:5 compare escape velocity of two planets

Answer 1

The escape velocity depends on mass M and radius r as

$mv^{2}/2=GmM/r$

$v=\sqrt{(}GM/r)$

Hence, ratio of escape velocities will be

$v1/v2=\sqrt{(}M1\cdot r2/M2\cdot r1)=\sqrt{(}5\cdot 10/2)=\sqrt{(}25)=5$