Given that,
Mass of ring = m
Mass of sphere = M
Radius = R
Distance = √8R
We need to calculate the intensity of gravitational field
Using formula of intensity
![E_{g}=\dfrac{Gmx}{\sqrt{(r^2+x^2)^\frac{3}{2}}}](https://tex.z-dn.net/?f=E_%7Bg%7D%3D%5Cdfrac%7BGmx%7D%7B%5Csqrt%7B%28r%5E2%2Bx%5E2%29%5E%5Cfrac%7B3%7D%7B2%7D%7D%7D)
Put the value into the formula
![E_{g}=\dfrac{Gm\sqrt{8}R}{(R^2+8R^2)^{\frac{3}{2}}}](https://tex.z-dn.net/?f=E_%7Bg%7D%3D%5Cdfrac%7BGm%5Csqrt%7B8%7DR%7D%7B%28R%5E2%2B8R%5E2%29%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%7D)
![E_{g}=\dfrac{2\sqrt{2}Gm}{(9R^2)^{\frac{3}{2}}}](https://tex.z-dn.net/?f=E_%7Bg%7D%3D%5Cdfrac%7B2%5Csqrt%7B2%7DGm%7D%7B%289R%5E2%29%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%7D)
![E_{g}=\dfrac{2\sqrt{2}Gm}{27R^2}](https://tex.z-dn.net/?f=E_%7Bg%7D%3D%5Cdfrac%7B2%5Csqrt%7B2%7DGm%7D%7B27R%5E2%7D)
We need to calculate the force of attraction between the ring and the sphere
Using formula of attraction force
![F=M\times E_{g}](https://tex.z-dn.net/?f=F%3DM%5Ctimes%20E_%7Bg%7D)
Where, M = mass of sphere
E = intensity of gravitational field
Put the value into the formula
![F=\dfrac{2\sqrt{2}GmM}{27R^2}](https://tex.z-dn.net/?f=F%3D%5Cdfrac%7B2%5Csqrt%7B2%7DGmM%7D%7B27R%5E2%7D)
Hence, The force of attraction between the ring and the sphere is ![\dfrac{2\sqrt{2}GmM}{27R^2}](https://tex.z-dn.net/?f=%5Cdfrac%7B2%5Csqrt%7B2%7DGmM%7D%7B27R%5E2%7D)