Question

What happens to the gravitational force between two masses when the distance between the masses is doubled?

Answer 1

Answer:

It decreases by a factor of 4

Explanation:

The gravitational force between two masses is given by

$F=\frac{Gm_1 m_2}{r^2}$

where

G is the gravitational constant

m1, m2 are the two masses

r is the separation between the two masses

In this problem, the distance between the masses is doubled, so

r' = 2r

Substituting into the equation, we see that the new force is

$F'=\frac{Gm_1 m_2}{(2r)^2}=\frac{1}{4}\frac{Gm_1m_2}{r^2})\frac{F}{4}$

So, the force decreases by a factor of 4.