A large vessel contains two immiscible liquids of densities d and 2d, each of height H/2. A homogeneous solid cylinder of length L

Question

A large vessel contains two immiscible liquids of densities d and 2d, each of height H/2. A homogeneous solid cylinder of length L < H/2 and cross-sectional area A/5 floats vertically across the liquid-liquid interface, with L/4 in the denser liquid. Find the density of the cylinder. Image

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G1 Physics · Accepted Answer

Step 1: Apply Archimedes' principle, Fᵦ = ρfluid g Vdisplaced, together with force/torque equilibrium. Step 2: Use the immersed volume from the given geometry and solve the balance condition. Applying these relations to the given data gives A: 5d/4. Final answer: A.