A uniform ring of mass m and radius a is placed directly above a uniform sphere of mass M and of equal to radius of ring. The centre of the ring is at a distance 3 a from the centre of the sphere as shown in figure . The gravitational force

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

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Correct answer: A. 3 G M m 8 a 2

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

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

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