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A wooden cylinder of length l floats ver...

A wooden cylinder of length l floats vertically in a liquid of specific gravity `rho` with `((1)/(3))^(rd)` part of its length submerged. Another liquid that is immiscible with the previous liquid is poured into it, to just completely submerge the cylinder. If the density of the liquid at the bottom, density of cylinder and density of upper liquid are in G.P., find the fraction of the cylinder submerged in lower liquid.

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`(1)/(4)`
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