contestada

If the gravitational force between two masses located a distance 100 m apart is F, what would be the force between these objects if the distance between them increases to 800 m?

Respuesta :

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]