Gravitation

A uniform sphere $A$ with radius $R$ exerts a force $F$ on a small particle $B$ situated at a distance $2 R$ from the centre of the sphere. A spherical portion of diameter $R$ is cut from the sphere $A$ as shown in the figure. If $F^{\prime}$ is the new gravitational force between the remaining part of the sphere $A$ and the particle $B$, then the correct relation between $F$ and $F^{\prime}$