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
[tex]E_{g}=\dfrac{Gmx}{\sqrt{(r^2+x^2)^\frac{3}{2}}}[/tex]
Put the value into the formula
[tex]E_{g}=\dfrac{Gm\sqrt{8}R}{(R^2+8R^2)^{\frac{3}{2}}}[/tex]
[tex]E_{g}=\dfrac{2\sqrt{2}Gm}{(9R^2)^{\frac{3}{2}}}[/tex]
[tex]E_{g}=\dfrac{2\sqrt{2}Gm}{27R^2}[/tex]
We need to calculate the force of attraction between the ring and the sphere
Using formula of attraction force
[tex]F=M\times E_{g}[/tex]
Where, M = mass of sphere
E = intensity of gravitational field
Put the value into the formula
[tex]F=\dfrac{2\sqrt{2}GmM}{27R^2}[/tex]
Hence, The force of attraction between the ring and the sphere is [tex]\dfrac{2\sqrt{2}GmM}{27R^2}[/tex]
