Two steel spheres of radius r and 2r are made to touch each other. The distance of their centre of mass from their point of contact is 

Given,

First sphere's radius = r.

The second sphere's radius = 2r.

We know that,

M = ρV

If the larger sphere's centre serves as the origin

hence, the mass's centre

$\mathrm{CM}=\frac{{\mathrm{m}}_1{\mathrm{x}}_1+{\mathrm{m}}_2{\mathrm{x}}_2}{{\mathrm{m}}_1+{\mathrm{m}}_2}$

$\mathrm{CM}=\frac{\mathrm{\rho }{\displaystyle \frac{4}{3}}\mathrm{\pi }{\left(2\mathrm{r}\right)}^3\times 0+\mathrm{\rho }\frac{4}{3}\mathrm{\pi }{\left(\mathrm{r}\right)}^3\times 3\mathrm{r}}{\mathrm{\rho }\frac{4}{3}\mathrm{\pi }{\left(2\mathrm{r}\right)}^3+\mathrm{\rho }\frac{4}{3}\mathrm{\pi }{\left(\mathrm{r}\right)}^3}$

$\mathrm{CM}=\frac{3}{9}\mathrm{r}=\frac{\mathrm{r}}{3}$

This distance is from the centre of the larger sphere. therefore, C.O.M will be at 5r/3 away from the point of contact.