If earth has amass 9 times and radius 4 times than that of a planet 'P'. Calculate the escape velocity of the planet P if its value on earth is 11.2 km/s.

The escape velocity is given as

v= [2GM/R]^1/2 

now,

for earth

v_e = [2GM_e/R_e]^1/2 

or v_e = 11.2km/s 

for planet

v_p = [2GM_p/R_p]^1/2 

and we have

M_p = (1/9)M_e
R_p = (1/4)R_e

so,

v_p = [2G(1/9)M_e / (1/4)R_e]^1/2 
or
v_p = (2/3).[2GM_e / R_e]^1/2 
so,
v_p = (2/3).v_e = 0.66 x 11.2
thus,
escape velocity of planet will be
v_p = 7.4 km/s