As shown in the figure,two spherical cavities are made in a 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

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