We know that the gravitational force between two masses is given by:
[tex]F=G\frac{mM}{r^2}[/tex]where r is the distance between the masses. If the distance is half of the original one, we have:
[tex]\begin{gathered} F^{\prime}=G\frac{mM}{(\frac{r}{2})^2} \\ F^{\prime}=G\frac{mM}{\frac{r^2}{4}} \\ F^{\prime}=4(G\frac{mM}{r^2}) \\ F^{\prime}=4F \end{gathered}[/tex]Therefore, the new force will be four times the original one and the answer is A.
