contestada

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

Respuesta :

Answer:

F' = F/16

Explanation:

The gravitational force between masses is given by :

[tex]F=G\dfrac{m_1m_2}{r^2}[/tex]

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

New force will be :

[tex]F'=G\dfrac{m_1m_2}{r'^2}\\\\F'=G\dfrac{m_1m_2}{(4r)^2}\\\\F'=\dfrac{Gm_1m_2}{16r^2}\\\\F'=\dfrac{1}{16}\times \dfrac{Gm_1m_2}{r^2}\\\\F'=\dfrac{F}{16}[/tex]

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