Question

What happens to the force of two objects if the distance between the objects is doubled?

Answer 1

Dear student,
$$\begin{gathered} FromNewton\text{'}slawofGravitation,weknow \\ F=\frac{GMm}{r^2} \\ WhereMandmarethemassoftwoobjects,risthedis\tan cebetweenthemandGistheuniversalgraviationacons\tan t \\ then, \\ F\propto \frac{1}{r^2} \\ soiftherbecomesdouble,i.e.r\text{'}=2r \\ then, \\ F\text{'}\propto \frac{1}{{(r\text{'})}^2} \\ then, \\ \frac{F\text{'}}{F}=\frac{r^2}{{(r\text{'})}^2}=\frac{r^2}{4r^2}=\frac{1}{4} \\ then, \\ F\text{'}=\frac{F}{4} \\ thatisforcebecomesoneforthoftheoriginalvalue. \end{gathered}$$
Regards,