Two solid metal spheres of same material having density $\rho$ and each of radius ‘r’ are kept in contact with each other. The gravitational force (F) between them  is 

Let the density of the material as $\rho$,

And Radius = r

We know that, mass= volume X density
Therefore, the mass of both spheres will be:

${\text{m}}_1=\frac{4}{3}\pi {\text{r}}^{\text{3}}\rho$ ,  ${\text{m}}_2=\frac{4}{3}\pi {\text{r}}^{\text{3}}\rho$
Let's find the force between the two spheres:
Distance between the two spheres can be taken as:
$\text{d}=2\text{r}$

We know

$\text{F}=\frac{\text{G}{\text{.m}}_{\text{1}}{\text{m}}_{\text{2}}}{{\text{d}}^{\text{2}}}$

$\text{F}=\frac{\text{G}.\frac{4}{3}\pi {\text{r}}^{\text{3}}\rho \times \frac{4}{3}\pi {\text{r}}^{\text{3}}\rho }{{\left(\text{2r}\right)}^{\text{2}}}$

$\text{F}=G.\frac{16}{9}\frac{{\pi }^2{r}^6{\rho }^2}{4{\text{r}}^{\text{2}}}$

$\text{F}=\frac{4}{9}G{\pi }^2{r}^4{\rho }^2$
Therefore, option D is the correct answer.