A spherical hole of radius R/2 is excavated from the asteroid of mass as shown in the figure. The gravitational acceleration at a point on the surface of the asteroid just above the excavation is

Lets assume this is a combination of two spheres of radius R and R/2. 

where the sphere R/2 is considered of negative mass.

The mass of the sphere with radius R/2

${\mathrm{m}}^{\text{'}}=\frac{\mathrm{m}}{\left(\frac{4\mathrm{\pi }}{3}{\mathrm{R}}^3\right)}\times \frac{4\mathrm{\pi }}{3}\frac{{\mathrm{R}}^3}{8}=\frac{\mathrm{m}}{8}$

$\mathrm{g}=\frac{\mathrm{Gm}}{{\mathrm{R}}^2}-\frac{\mathrm{G}{\displaystyle \frac{\mathrm{m}}{8}}}{{\left({\displaystyle \frac{\mathrm{R}}{2}}\right)}^2}=\frac{\mathrm{Gm}}{2{\mathrm{R}}^2}$