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

Point of contact is treated as origin:

${\mathrm{X}}_{\mathrm{cm}}=\frac{{\mathrm{M}}_1{\mathrm{X}}_1+{\mathrm{M}}_2{\mathrm{X}}_2}{{\mathrm{M}}_1+{\mathrm{M}}_2}= \frac{{\mathrm{V}}_1{\mathrm{X}}_1+{\mathrm{V}}_2{\mathrm{X}}_2}{{\mathrm{V}}_1+{\mathrm{V}}_2}$     (Since, M $\propto$ V)

${\mathrm{X}}_{\mathrm{CM}}=\frac{\left({\displaystyle \frac{4}{3}}{\mathrm{\pi r}}^2\mathrm{\rho }\right)(-\mathrm{r})+{\displaystyle \frac{4}{3}}\mathrm{\pi }\left(8{\mathrm{r}}^3\right)\mathrm{\rho }\left(2\mathrm{r}\right)}{\frac{4}{3}{\mathrm{\pi r}}^3\mathrm{\rho }+\frac{4}{3}\mathrm{\pi }\left(8{\mathrm{r}}^3\right)\mathrm{\rho }}$

$=\frac{15\mathrm{r}}{9}=\frac{5\mathrm{r}}{3}$
CM is at a distance 5r/3 in bigger sphere.