Question

A rectangular piece of wood floats in water of density 1000kg/m^3 . Bath oil of density 300kg/m^3 is slowly added, forming a layer that does not mix with the water. When the top surface of the oil is at the same level as the top surface of the wood, the ratio of the oil layer thickness to the wood’s thickness, x/L = 4/7 . What is the density of the wood?

Answer 1

Mass = density * volume = ρ V

Mass of wood = Mass Water + Mass Oil (multiply by g to get weight)

Vw ρw = 3/7 V (1000 kg/m^3) + 4/7 V 300 kg/m^3)

Let V be 1

ρw = (3000 + 1200) kg/m^3/ 7 = 600 kg/m^3

Density = 600 kg/m^3