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A solid cube floats in a liquid of density rho with half of its volume submerged as shown. The side length of the cube is a, which is very small compared to the size of the container. Now a liquid of density (rho)/(3) (immiscible with the liquid already in the container) is poured slowly into the container. The column of the liquid of density (rho)/(3) that must be poured so that the cube is fully submerged (with its top surface coincident with the surface of the poured liquid) is : |
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Answer» `(a)/(3)` Then, because cube is in equilibrium `rho_(o)a^(3)G=rho((a^(3))/(2))g` `impliesrho_(o)=(rho)/(2)` Let the final equilibrium POSITION of the cube be as SHOWN Then, `rho_(o)a^(3)g=((rho)/(3))(a^(2)x)g+rho(a-x)(a^(2))g` `impliesx=(3)/(4)a` 
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