Final answer:
To find the density of the object and the other liquid, we use the change in weight of the object when submerged in water and the unknown liquid, applying Archimedes' principle. The buoyant forces are used to calculate the volume of the object and then its density. The same approach is used to determine the density of the other liquid.
Step-by-step explanation:
To determine the density of the object and the other liquid, we start by noting the differences in weight when the object is in air and when it's submerged in water and the other liquid. The weight of an object in air minus the weight when submerged gives us the buoyant force, which is equal to the weight of the fluid displaced by the object based on Archimedes' principle.
When submerged in water (density of 1000 kg/m³), the weight changes from 15N to 12N, giving a buoyant force of 3N. This force equals the weight of the water displaced. We can use the weight of the displaced water to find the volume of the object, since density is mass/volume and weight is mass x gravity (where gravity is 9.8 m/s²). The volume V can be calculated by: V = weight of displaced water / (density of water x gravity).
Once we have the volume of the object, we can calculate its density using the weight of the object in air divided by its volume. Similarly, we calculate the density of the other liquid by finding the buoyant force when the object is submerged in it, which will be the weight in air minus the weight in liquid, and then using the object's volume to find the liquid's density.