A uniform ring of mass \[m\] and radius r is placed directly above a uniform sphere of mass \[M\] and of equal radius. The centre of the ring is directly above the centre of the sphere at a distance \[r\sqrt{3}\]\[r\] as shown in the figure. The gravitational force exerted by the sphere on the ring will be

• A. \[\frac{GMm}{8{{r}^{2}}}\]   
• B. \[\frac{GMm}{4{{r}^{2}}}\]
• C. \[\sqrt{3}\frac{GMm}{8{{r}^{2}}}\]   
• D. \[\frac{GMm}{8{{r}^{2}}\sqrt{3}}\]