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How does the force of gravitation between two objects change when the distance between them is reduced to half?

Q. 1.     How does the force of gravitation between two objects change when the distance between them is reduced to half?

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S Sayak

Let there be two bodies of masses m1 and m2 and let the distance between them be r. The gravitational force F between them would be given by

F_{}=G\frac{m_{1}m_{2}}{r^{2}}

Let the distance between them be halved by two. The gravitational force between them would now be given by

\\F'=G\frac{m_{1}m_{2}}{(\frac{r}{2})^{2}}\\ F'=4G\frac{m_{1}m_{2}}{r^{2}}\\ F'=4F

The force of gravitation between two objects would increase by 4 times if the distance between them is halved.

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