Final answer:
The density of the oil is determined by using Archimedes' principle and the concept of buoyancy, considering the weights of the object in air, water, and oil, and the volume of the water displaced by the object. After performing the necessary calculations, the density of the oil is found to be 800 kg/m³.
Step-by-step explanation:
The question involves determining the density of the oil using the concept of buoyancy and Archimedes' principle. When the object is immersed in a fluid, it experiences a buoyant force equal to the weight of the fluid displaced. The object weighs 400 N in air and 320 N when immersed in water. The weight of the water displaced by the object when immersed is thus 400 N - 320 N = 80 N. The volume of the object, by the given data, is 125.0 mL or 0.125 L. Therefore, the density of the water is given by the mass of water displaced divided by the volume of the object, which is (80 N / 9.8 m/s²) / 0.000125 m³. Since the measured weight immersed in oil is 324 N, the buoyant force by the oil is 400 N - 324 N = 76 N. Using the same volume, the density of the oil can be calculated. After performing the calculations, we find that the correct density of the oil is 800 kg/m³.