Two immiscible liquids of densities ρ and nρ (n > 1) each have height h in a container. A uniform solid cylinder of length L and density d floats vertically with length pL (0 < p < 1) immersed in the denser liquid. Find d.
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Question

Two immiscible liquids of densities ρ and nρ (n > 1) each have height h in a container. A uniform solid cylinder of length L and density d floats vertically with length pL (0 < p < 1) immersed in the denser liquid. Find d.

Options

G1 Physics · Accepted Answer

Step 1: Let cross-sectional area of cylinder be A. Mass of cylinder is dAL. Step 2: Length pL is in the lower liquid of density nρ; the remaining length (1 − p)L is in the upper liquid of density ρ. Step 3: Total buoyancy = ρgA(1 − p)L + nρgApL. Step 4: For floating equilibrium, dALg = ρAgL[(1 − p) + np]. Step 5: Divide by ALg: d = ρ[1 − p + np] = ρ[1 + (n − 1)p]. Final answer: ρ[1 + (n − 1)p] (Option D).