A uniform ring of mas m and radius a is placed directly above a uniform sphere of mass M and of equal radius. The centre of the ring is at a distance `sqrt3` a from the centre of the sphere. Find the gravitational force exerted by the sphere on the ring.

Explanation

Gravitational field due to ring at centre of sphere
`E=(Gm(sqrt(3)a))/([(sqrt(3)a)^(2)+a^(2)]^(3//2))=(sqrt(3)Gma)/((4a^(2))^(3//2))`
`=(sqrt(3)Gma)/(8a^(3))=(sqrt(3)Gm)/(8a^(2))`
Force on sphere
`F=ME=(sqrt(3)GMm)/(8a^(2))`
The same force sphere exerts on the ring.