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Ques: A uniform ring of mass M & radius R is placed directly above a uniform sphere of mass 8M & radius R. The centre of ring is at a distance of d=√3R from the centre of the sphere. The gravitational attraction between the sphere and ring is

Solution:

Gravitational field due to ring at a distance

d=3–√Rd=3R on its axis is

E=GMd/(R^2+d^2)^3/2

=√3GM/8R^2

Force on the sphere = mass of sphere × E

=8ME

Hence, Force =√3GM^2/R^2

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