Final answer:
The maximum depth to which the body sinks is determined by the initial potential energy being transformed to potential energy at depth, with buoyancy considered. The correct formula is height dropped times the object's density divided by the difference in densities of object and liquid. So the answer is A. hrho/σ-ρ.
Step-by-step explanation:
The question involves a concept from physics concerning the behavior of an object submerged in a fluid with different density. When an object is dropped into a liquid, it will sink until the buoyant force equals the weight of the object.
The buoyant force can be calculated using the volume of the fluid displaced by the submerged part of the object and the density of the fluid (Archimedes' principle). In this case, the object has a density ρ and it is dropped into a lake with a denser liquid of density σ (σ > ρ). The ratio of densities (ρ/σ) describes what fraction of the object’s volume needs to be submerged to displace a weight of water equal to its own. Therefore, the maximum depth to which the body will sink is given by the initial potential energy (mgh) being converted into the potential energy at depth (mgD), considering the buoyancy effect.
The correct formula, considering these factors, will be the height the object sinks (D) multiplied by its density (ρ), equal to the height it was dropped from (h), multiplied by the difference in densities (σ - ρ). Simplified, we find that the maximum depth D is given by hρ/(σ-ρ), thus answer A. hrho/σ-ρ is correct.