Answer to Question #102215 in Physics for Nyx

Question

Oil having a density of 928 kg/m3 floats on
water. A rectangular block of wood 3.97 cm
high and with a density of 974 kg/m3 floats
partly in the oil and partly in the water. The
oil completely covers the block.
How far below the interface between the
two liquids is the bottom of the block?
Answer in units of m.

Answer 1

For the equilibrium:

$$\rho_{wood}gh-\rho_{oil}g(h-x)-\rho_{water}gx=0$$

$$\rho_{wood}h-\rho_{oil}(h-x)-\rho_{water}x=0$$

$$(974)(3.97)-928(3.97-x)-1000x=0$$

$$x=2.54\ cm$$