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When placed inside a liquid of density $$d_1$$, a sphere sinks as shown in figure
i. When placed inside a liquid of density $$d_2$$, the same sphere floats with half of its volume above the liquid surface as shown in figure ii. Given that the density of the sphere is $$d$$.

If $$F_1$$ and $$F_2$$ are the buoyant forces in the two situations, then the ratio $$F_1/F_2$$ equals
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