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Question

# A uniform ring of mass ‘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 √3a from the centre of the sphere. The gravitational force exerted by the sphere on the ring is

A
GMm8a2
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B
8GMm3a2
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C
3GMm8a2
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D
GMm3a2
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Solution

## The correct option is C √3GMm8a2The gravitational field due to the ring at a distance $$d = \sqrt {3}a$$ on its axis is E=Gmd(a2+d2)32=√3Gm8a2 The force on a particle of mass ‘M’ placed here is F = ME ⇒F=√3GMm8a2 This is also the force due to the sphere on the ring.

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