31. The gravitational force between two bodies is inversely proportional to the square of the distancebetween the bodies. Suppose two objects 12 kilometers apart are attracted b…

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asked Feb 15, 2023 189k views

1 Answer

Michael Barton · Answer 1 · 2023-02-21T02:44:11+0000

From the question the gravitational force G between two bodies is inversely proportional to the square of the distance d between the bodies.

$G\propto(1)/(d^2)$

using the constant of proportionality k, we have;

$\begin{gathered} G=(k)/(d^2) \\ k=Gd^2 \end{gathered}$

Given;

$\begin{gathered} d_1=12\operatorname{km} \\ G_1=40N \end{gathered}$

Substituting this value to derive the value k;

$\begin{gathered} k=Gd^2 \\ k=40(12)^2 \\ k=5760 \end{gathered}$

So, for distance of 8 km, the gravitational force between the bodies is;

$\begin{gathered} d_2=8\operatorname{km} \\ G_2=(k)/(d^2)=(5760)/((8)^2) \\ G_2=90N \end{gathered}$

Therefore, the gravitational force between the objects when they are 8 kilometers apart is 90N