From a sphere of mass M and radius R , a smaller sphere of radius $\;\large\frac{R}{2}\;$ is carved out such that the cavity made in the original sphere is between its centre and the periphery . (See figure) . For the configuration in the figure where the distance between the centre of the original sphere and the removed sphere is 3R , the gravitational force between the two spheres is :

Question

$(a)\;\large\frac{41GM^{2}}{3600R^{2}} \qquad(b)\;\large\frac{41GM^{2}}{450R^{2}} \qquad(c)\;\large\frac{59GM^{2}}{450R^{2}} \qquad(d)\;\large\frac{GM^{2}}{225R^{2}}$