Question

If mass of planet is 8 times the mass of the earth and it's radius twice the radius of earth what will be the ratio of escape velocity on the surface of earth to the escape velocity on the planet

Answer 1

Answer:

$\frac{1}{2}$

Explanation:

Let,

m = mass of earth

M = mass of planet

r = radius of earth

R = radius of planet

It is given that

                                M = 8m

        and                  R = 2r

escape velocity is given by:

                                 v = $\sqrt{2Gm/r}$                   (for earth)

and                           v' = $\sqrt{16Gm/2r}$              (for planet)

Dividing both equations

                                  $\frac{v}{v'}$ = $\frac{1}{2}$