Two concentric spherical shells of masses $M_1$ and $M_2$ have uniform density $\sigma$. These two spherical shells behave as if their masses $M_1$ and $M_2$ are concentrated at their common centre.

(i) At the point r=a:

The magnitude of the gravitational fields at r=a due to $M_1$ and $M_2$ are $\frac{GM_1}{a^2}$ and $\frac{GM_2}{a^2}$ respectively, both are directed along the line joining the common centre and the point $r=a$. [where $G$ is the gravitational constant.]

Hence the magnitude of the resultant field is $\frac{G(M_1+M_2)}{a^2}$. So the force on the particle of mass $m$, placed at the point $a$ is $\frac{G(M_1+M_2)}{a^2}\cdot{m}$.

(ii) At the point r=b:

The point $r=b$ is an external point with respect to the shell $M_2$ and an internal point with respect to the shell $M_1$. Since the gravitational field intensity at an internal point due to a shell is zero. So here the gravitational field intensity at $r=b$ is due to only shell $M_2$ which behaves as if its entire mass is at centre. The magnitude of the gravitational field intensity is $\frac{GM_2}{b^2}$. Now the force on the particle of mass $m$ at $r=b$ is $\frac{GM_2}{b^2}\cdot{m}$.

(iii) At the point r=c:

The point $r=c$ is the internal point due to the both shells $M_1$ and $M_2$. Since the gravitational field intensity at a point inside the shell is zero, So the gravitational field intensity at the point $r=c$ due to the both shells is $zero$.