A rectangular block of height L and cross-sectional area A floats at the interfa

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A rectangular block of height L and cross-sectional area A floats at the interface between two immiscible liquids, as shown below Derive a formula for the block density, rhos in terms of the fluid densities rho1 and rho2, the heights ho, h1, and h2, and the cross-sectional area A. (It is not necessary that all of these variables appear in the final result.). Force balances on the block can be calculated in two ways: (i) in terms of the weight of the block and the hydrostatic forces on the upper and lower block surfaces; and (ii) in terms of the weight of the block and the buoyant force on the block as expressed by Archimetes' principle. Prove that these two approaches are equivalent.

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