Two objects of equal masses placed at certain distance from each...

The gravitational force between particles is given by, $F = \dfrac{G{m}_{1}{m}_{2}}{{r}^{2}}$

$∵ F = \dfrac{G{m}^{2}}{{r}^{2}}$

When one-third mass is transferred to other object

${m}_{1} = \dfrac{2m}{3}, {m}_{2} = \dfrac{4m}{3}$

${F}_{2} = \dfrac{8G{m}^{2}}{9{r}^{2}}$

$⇒ {F}_{2} = \dfrac{8}{9}F$