The gravitational force of attraction between the ring and sphere as shown in the diagram $\frac{\sqrt{x}}{27} \frac{G M m}{R^{2}}$ where the plane of the ring is perpendicular to the line joining the centres. If $\sqrt{8} R$ is the distance between the centres of a ring (of mass ‘m’) and a sphere (mass ‘M’) where both have equal radius ‘R’. Then find the value of $x$

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Detailed Solution

Gravitational field of ring $E = \frac{- G m x}{{(R^{2} + x^{2})}^{3 / 2}}$

Force between sphere and ring , $F = \frac{G M m \sqrt{8} R}{{[R^{2} + 8 R^{2}]}^{3 / 2}}$

$\Rightarrow F = \frac{\sqrt{8} G M m}{27 R^{2}}$

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