A solid sphere of uniform density and radius $R$ applies a gravitational force of attraction equal to $F_1$ on a particle placed at a distance $3R$ from the centre of the sphere. A spherical cavity of the radius $\raisebox{1ex}{$R$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ is now made in the sphere as shown in the figure. The sphere with the cavity now applies a gravitational force $F_2$ on the same particle. The ratio $\frac{F_2}{F_1}$ is