A ring of mass m and a sphere of mass M have the same radius R, and the distance between their centres is √8R. The plane of the ring is perpendicular to the line joining the centres, as shown in the diagram. Find the gravitational force of attraction between the ring and the sphere.

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Accepted Answer

(3) (√8)/(27)·(GmM)/(R²). On its own axis, at a distance x from its centre, a ring of mass m and radius R sets up a field E=(Gmx)/((x²+R²)^3/2). The sphere sits on that axis at x=√8R, so x²+R²=9R² and (x²+R²)^3/2=27R³. E=(Gm(2√2R))/(27R³)=(2√2Gm)/(27R²). A uniform sphere in an external field responds as if all its mass were at its centre, so F=ME=(√8)/(27)·(GmM)/(R²).

A ring of mass m and a sphere of mass M have the same radius R, and the distance between their centres is √8R. The plane of the ring is perpendicular to the line joining the centres, as shown in the diagram. Find the gravitational force of attraction between the ring and the sphere.

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