Answer:
[tex] \frac{F}{64}[/tex]
Explanation:
m = product of masses of two objects
r = distance between the two objects = 100 m
F = initial force between the two object
r' = new distance between the two objects = 800 m
F' = new force between the two objects = ?
k = constant of proportionality
initial force between the two object is given as
[tex]F=\frac{km}{r^{2}}[/tex] eq-1
new force between the two objects is given as
[tex]F'=\frac{km}{r'^{2}}[/tex] eq-2
Dividing eq-2 by eq-1
[tex]\frac{F'}{F}=\frac{r^{2}}{r'^{2}}[/tex]
Inserting the values
[tex]\frac{F'}{F}=\frac{100^{2}}{800^{2}}[/tex]
[tex]F' = \frac{F}{64}[/tex]