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A body of density rho sinks in a liquid ...

A body of density `rho` sinks in a liquid of density `rho_(L)`.The densities `rho` and `rho_(L)` are related as:

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To solve the problem, we need to establish the relationship between the density of the body (ρ) and the density of the liquid (ρ_L) based on the information provided. ### Step-by-Step Solution: 1. **Understanding the Problem**: - We have a body with a density denoted as ρ. - The liquid in which the body is submerged has a density denoted as ρ_L. - The problem states that the body sinks in the liquid. 2. **Applying Archimedes' Principle**: - According to Archimedes' Principle, a body will float in a fluid if its density is less than the density of the fluid. Conversely, if the body sinks, its density must be greater than the density of the fluid. 3. **Establishing the Relationship**: - Since the body is sinking, we can conclude that the density of the body (ρ) is greater than the density of the liquid (ρ_L). - Mathematically, this can be expressed as: \[ \rho > \rho_L \] 4. **Conclusion**: - Therefore, the relationship between the densities is that the density of the body is greater than the density of the liquid. ### Final Answer: The relationship between the densities is: \[ \rho > \rho_L \]
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