By the principle of superposition of fields

$\overrightarrow{\text{E}}={\overrightarrow{\text{E}}}_1+{\overrightarrow{\text{E}}}_2$

Here, $\overrightarrow{\text{E}}$ = net field at the centre of hole due to entire mass

${\overrightarrow{\text{E}}}_1$ = field due to remaining mass

and  ${\overrightarrow{\text{E}}}_2$ = field due to mass in hole = 0

$\therefore {\text{E}}_1=\text{E}=\left(\frac{\text{GM}}{{\text{R}}^3}\right)\text{.}\text{r}$        where r $=\frac{\text{R}}{2}$

$\therefore \text{E}=\frac{\text{GM}}{2{\text{R}}^2}$