Question

two identical spheres each with a mass m and a distance r between their centres , exert a gravitational force of magnitude F on each other. The distance between their centres is halved . what is the magnitude of the force that the spheres exert on each other ?

Answer 1

The initial force:

$$F_i=G\frac{Mm}{r^2},\\\space\\ F_f=G\frac{Mm}{(r/2)^2},\\\space\\ \frac{F_f}{F_i}=4\space\rightarrow\space F_f=4F_i.$$

The force will increase fourfold.