Final answer:
Using Archimedes' Principle and the given buoyant forces in water and an unknown liquid, the density of the unknown liquid is calculated to be approximately 0.8 g/cm³, which corresponds to the answer choice D.
Step-by-step explanation:
The problem you've presented involves finding the density of an unknown liquid using the principle of buoyancy, as described by Archimedes' Principle. Since the body weighs 0.45 N in air and only 0.22 N when totally immersed in water, the buoyant force of water on the body is 0.45 N - 0.22 N = 0.23 N. Similarly, when the body is immersed in the unknown liquid, the weight is 0.26 N, so the buoyant force of this liquid is 0.45 N - 0.26 N = 0.19 N.
To find the density of the liquid, we realize that the buoyant forces are proportional to the densities of the fluids. Since we know the density of water is 1 g/cm³ (or equivalently, 1000 kg/m³), and the buoyant force due to water is 0.23 N, we can set up a proportion:
Buoyant force in water / Density of water = Buoyant force in unknown liquid / Density of unknown liquid
0.23 N / 1 g/cm³ = 0.19 N / Density of unknown liquid
Therefore, Density of unknown liquid = (0.19 N / 0.23 N) * 1 g/cm³ = 0.826 g/cm³ ≈ 0.8 g/cm³. The closest answer option that matches this calculation is D. 0.8 g/cm³.