Question

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

Answer 1

It decreases by a factor of 4

Step-by-step explanation:

The gravitational force between two masses is given by

`F=(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'=(Gm_1 m_2)/((2r)^2)=(1)/(4)(Gm_1m_2)/(r^2))(F)/(4)`

So, the force decreases by a factor of 4.