Question

HOMEWORK: The gravitational attractive force between two masses is F. If the masses are moved to half of their initial distance, what is the gravitational attractive force?A) 4FB) 2FC) F/2D) F/4

Answer 1

We know that the gravitational force between two masses is given by:

$F=G\frac{mM}{r^2}$

where r is the distance between the masses. If the distance is half of the original one, we have:

$\begin{gathered} F^{\prime}=G\frac{mM}{(\frac{r}{2})^2} \\ F^{\prime}=G\frac{mM}{\frac{r^2}{4}} \\ F^{\prime}=4(G\frac{mM}{r^2}) \\ F^{\prime}=4F \end{gathered}$

Therefore, the new force will be four times the original one and the answer is A.