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A uniform ring of mass M and radius R is placed directly above a uniform sphere of mass 8M and of same radius R. The centre of the ring is at a distance of $d = \sqrt{3} R$ from the centre of the sphere. The gravitational attraction between the sphere and the ring is

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$\frac{\sqrt{3} G M^{2}}{R^{2}}$

$\frac{8 G M^{2}}{R^{2}}$

$\frac{3 G M^{2}}{2 R^{2}}$

$\frac{2 G M^{2}}{\sqrt{3} R^{2}}$

answer is D.

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Detailed Solution

Gravitational field due to the ring at a distance d=√3 R on axis is
E = $\frac{G M d}{{(R^{2} + d^{2})}^{3 / 2}} = \frac{\sqrt{3} GM}{{8R}^{2}}$
Force on sphere = 8ME = $\frac{\sqrt{3} G M^{2}}{R^{2}}$

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