Question

The radius of Saturn is about 10 times the radius of Venus and the mass is about 100 times that of Venus. How much larger is the force of gravity on a person of mass m standing on the surface of the planet of Saturn compared to Venus?

Answer 1

let the mass of Venus is M then mass of Saturn is 100 M

similarly if the radius of Venus is R then the radius of Saturn is 10 R

now the force of gravity on a man of mass "m" at the surface of Venus is given by

$F_1 = \frac{GMm}{R^2}$

now similarly the gravitational force on the man if he is at the surface of Saturn

$F_2 = \frac{G*100M*m}{(10R)^2}$

$F_2 = \frac{GMm}{R^2}$

so here if we divide the two forces

$\frac{F_1}{F_2} = 1$

so here we can say

F1 = F2

so on both planets the gravitational force will be same