Two bodies are gravitationally attracted to one other. What would be the gravitational pull if the distance between their centers was reduced to half?

 

The equation for universal gravitation is given as: 

$\begin{array}{rcl}\mathrm{F}& =& \frac{{\mathrm{Gm}}_1{\mathrm{m}}_2}{{\mathrm{R}}^2}\end{array}$ here G= universal gravitational constant; m₁ and m₂ are the masses of the two bodies; R is the distance between the two bodies. 

Initial force $\begin{array}{rcl}\mathrm{F}& =& \frac{{\mathrm{Gm}}_1{\mathrm{m}}_2}{{\mathrm{R}}^2}\end{array}$

Therefore final force 

$F^{\text{'}}= \frac{G{m}_1{m}_2}{{\left(R^{\text{'}}\right)}^2}$ here $R^{\text{'}}= \frac{R}{2}$

$F^{\text{'}}= \frac{G{m}_1{m}_2}{{\left({\displaystyle \frac{R}{2}}\right)}^2}$

$F^{\text{'}}= \frac{4G{m}_1{m}_2}{{\left(R\right)}^2}$

$F^{\text{'}}= 4F$

As a result, the gravitational force will increase by four times.