There are two concentric spherical shells of masses $m_{1}and{m}_2$  and radii  $R_1$ and  $R_2$  $\left(R_2>R_1\right)$. The force on a particle of mass $m_0$ kept at a distance ‘r’ from the common centre is F. Then,

When $\mathrm{r}<{\mathrm{R}}_1$, the mass lies inside the smaller shell, 

According to shell theorem, force on the mass due to the shell will be zero. 

$\mathrm{F}=0$

When ${\mathrm{R}}_1<\mathrm{r}<{\mathrm{R}}_2$, 

Force due to the larger shell will be zero and force due to small shell will be

$\mathrm{F}=\frac{{\mathrm{Gm}}_1{\mathrm{m}}_0}{{\mathrm{r}}^2}$

When ${\mathrm{R}}_2<\mathrm{r}$

Force due to both shells will be 

$\mathrm{F}=\frac{{\mathrm{Gm}}_1{\mathrm{m}}_0}{{\mathrm{r}}^2}+\frac{{\mathrm{Gm}}_2{\mathrm{m}}_0}{{\mathrm{r}}^2}=\frac{\mathrm{G}({\mathrm{m}}_1+{\mathrm{m}}_2){\mathrm{m}}_0}{{\mathrm{r}}^2}$