Question

If the distance between the center of two objects is quadrupled. The gravitational

force between the two objects will change by a factor of:
1) 16
2) 0.25
3) 4
4) 0.0625

Answer 1

F' = F/16

Step-by-step explanation:

The gravitational force between masses is given by :

`F=G(m_1m_2)/(r^2)`

If the distance between the center of two objects is quadrupled, r' = 4r

New force will be :

`F'=G(m_1m_2)/(r'^2)\\\\F'=G(m_1m_2)/((4r)^2)\\\\F'=(Gm_1m_2)/(16r^2)\\\\F'=(1)/(16)* (Gm_1m_2)/(r^2)\\\\F'=(F)/(16)`

So, the new force will change by a factor of 16.