A uniform ring of mass m and radius a is placed directly above a uniform sphere of mass M and of equal to radius. The centre of the ring is at a distance 3 a from the centre of the sphere. The gravi

Question

A uniform ring of mass m and radius a is placed directly above a uniform sphere of mass M and of equal to radius. The centre of the ring is at a distance 3 ​ a from the centre of the sphere. The gravitational force ( F ) exerted by the sphere on the ring is

TestHub · Accepted Answer

Now, the gravitational field due to the ring at a distance d = 3 ​ a on its axis is E = ( a 2 + d 2 ) 3/2 G m d ​ = 8 a 2 3 ​ G m ​ The force in a particle of mass M placed here is F = ME = 8 a 2 3 ​ GM m ​ This is also the force due to the sphere in the ring.

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