Question

The gravitational attraction betweentwo bodies varies inversely as thesquare of the distance between them.If the force of attraction is 64 poundswhen the distance between the bodiesis 9 feet, what is the distance betweenthem when the force is 36 pounds?

Answer 1

The force for the case 1 is 64 pounds and the distance is 9 feet, it is:

$\begin{gathered} \frac{k}{9^2}=64 \\ k=5184 \end{gathered}$

Now, if the force is 36 pounds, let solve for the distance:

$\begin{gathered} \frac{k}{r^2}=36 \\ \frac{5184}{r^2}=36 \\ r^2=144 \\ r=12 \end{gathered}$

Hence the answer is 12 feet.