Q1 . if earth has a mass 9 times and radius 2 times that of mars , calculate the minimum speed required by a rocket to pull out of gravitational force of mars .take the escape speed on the surface of earth to be 11.2 km/s

escape speed is given as

v = (2GM / R)^1/2

here

M is the mass of the planet

R is the radius of the planet

now, for Mars

v_m = (2GM_m / R_m)^1/2

for earth

v_e = (2GM_e / R_e)^1/2 = 11.2 km/s

we are given

M_m = M_e/9

and R_m = R_e/2

thus, we have

v_m = (2GM_m / R_m)^1/2 =  (2G(M_e /9) /  (R_e/2))^1/2

or

v_m = (2/9)^1/2 . (2GM_e / R_e)^1/2 = (2/9)^1/2.v_e

thus,

v_m = 0.4714 x v_e

or

v_m = 0.4714 x 11.2

so, the escape speed of Mars will be

v_m = 5.27 km/s