A rectangular block of height L and horizontal cross-sectional area A floats at the interface between two immiscible liquids, as shown below.

(a) Derive a formula for the block density, p_b, in terms of the fluid densities p₁ and p₂, the heights h₀, h₁, and h₂, and the cross-sectional area A. (It is not necessary that all of these variables appear in the final result).?

(b) Force balances on the blocks 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 Archimedes? principle. Prove that these two approaches are equivalent.

Fluid 1 P (g/cm) L Fluid 2 D(g/cm) | || | Block P. (g/cm)