Question

the gravitational force between two bodies is 100 newton. how should the distance be changed so that force brcome 50 newtons

Answer 1

$$\begin{gathered} \mathrm{Gravitational}\mathrm{force}\mathrm{is}\mathrm{inversely}\mathrm{proportional}\mathrm{to}\mathrm{the}\mathrm{square}\mathrm{of}\mathrm{distance}\mathrm{between} \\ \mathrm{the}\mathrm{given}\mathrm{objects}: \\ \mathrm{F}\mathrm{\alpha }\frac{1}{{\mathrm{r}}^2} \\ \frac{{\mathrm{F}}_2}{{\mathrm{F}}_1}={\left(\frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}\right)}^2 \\ \frac{{\mathrm{r}}_2}{{\mathrm{r}}_1}=\sqrt{\frac{{\mathrm{F}}_1}{{\mathrm{F}}_2}} \\ =\sqrt{\frac{100}{50}} \\ =\sqrt{2} \\ {\mathrm{r}}_2=\sqrt{2}{\mathrm{r}}_1 \\ \mathrm{The}\mathrm{distance}\mathrm{between}\mathrm{the}\mathrm{bodies}\mathrm{should}\mathrm{increase}\mathrm{to}\sqrt{2}\mathrm{times}\mathrm{of}\mathrm{the}\mathrm{original} \\ \mathrm{distance}. \end{gathered}$$