A  spherical  cavity  is  created  in  a  uniform  solid  sphere  of  mass  M  and  radius  R  by removing a part of sphere. The radius of the cavity is r & its centre is at a distance ‘a’ from the centre of the sphere.

$$\begin{gathered} Consider superposition of complete sphere of mass M and radius R \\ and for cavity take negative mass \left(\frac{M}{R^3}{r}^3\right) and radius r. \\ \overrightarrow{g}=\frac{GM}{R^3}\left(\overrightarrow{a}+\overrightarrow{r}\right)-\frac{G\left({\displaystyle \frac{M}{R^3}}{r}^3\right)}{r^3}\overrightarrow{r}=\frac{GM}{R^3}\overrightarrow{a} \\ Gravitational field is independent of location of point in cavity or we can say \\ the field is uniform inside the cavity. \end{gathered}$$