As shown in the figure, two spherical cavities are made in the uniform solid sphere of radius \(R\). The boundaries of the cavities touch at the centre of the sphere. The centers of the cavities and the sphere lie on the \(X\)-axis. The mass of the solid sphere before the cavities were created was \(M\). The gravitational force on a point mass \(m\) at a distance \(d\) away from the centre of the solid sphere is

1. A \(\frac{G M m}{d^2}\left[1-\frac{1}{8} \frac{1}{\left(1+\frac{R}{2 d}\right)^2}-\frac{1}{8} \frac{1}{\left(1-\frac{R}{2 d}\right)^2}\right]\)
2. B \(\frac{G M m}{d^2}\left[1-\frac{1}{8} \frac{1}{\left(1+\frac{R}{d}\right)^2}-\frac{1}{8} \frac{1}{\left(1-\frac{R}{d}\right)^2}\right]\)
3. C \(\frac{G M m}{d^2}\left[1-\frac{1}{8} \frac{1}{\left(1+\frac{d}{R}\right)^2}-\frac{1}{8} \frac{1}{\left(1-\frac{d}{R}\right)^2}\right]\)
4. D \(\frac{G M m}{d^2}\left[1-\frac{1}{8} \frac{1}{\left(1+\frac{d}{R}\right)^2}+\frac{1}{8} \frac{1}{\left(1-\frac{d}{R}\right)^2}\right]\)