Here are the formulas for relative density: Relative density (RD), also known as specific gravity, is a dimensionless quantity that is the ratio of the density of a substance to the density of a given reference material. For liquids and solids, the reference material is typically water at $4^\circ\text{C}$ (or sometimes at room temperature), which has a density of $1000 \text{ kg/m}^3$ or $1 \text{ g/cm}^3$. 1. Using Densities: The most fundamental formula for relative density is the ratio of the density of the substance to the density of the reference substance. $$\text{RD} = \frac{\rho_{\text{substance}}}{\rho_{\text{reference}}}$$ Where: • $\rho_{\text{substance}}$ is the density of the substance • $\rho_{\text{reference}}$ is the density of the reference substance (e.g., water) 2. Using Masses (for equal volumes): Since density ($\rho$) is mass ($m$) divided by volume ($V$), if we consider equal volumes of the substance and the reference material, the formula can be expressed in terms of mass: $$\text{RD} = \frac{m_{\text{substance}}}{m_{\text{reference}}}$$ Where: • $m_{\text{substance}}$ is the mass of a certain volume of the substance • $m_{\text{reference}}$ is the mass of an equal volume of the reference substance 3. Using Weights (for equal volumes): Similarly, since weight ($W$) is mass ($m$) times the acceleration due to gravity ($g$), if we consider equal volumes, the formula can be expressed in terms of weight: $$\text{RD} = \frac{W_{\text{substance}}}{W_{\text{reference}}}$$ Where: • $W_{\text{substance}}$ is the weight of a certain volume of the substance • $W_{\text{reference}}$ is the weight of an equal volume of the reference substance 4. For a substance immersed in a fluid (Archimedes' Principle): When a substance is weighed in air and then weighed while fully immersed in a fluid (like water), the apparent loss of weight is equal to the weight of the fluid displaced. $$\text{RD} = \frac{\text{Weight of substance in air}}{\text{Apparent loss of weight in water}}$$ $$\text{RD} = \frac{W_{\text{air}}}{W_{\text{air}} - W_{\text{water}}}$$ Where: • $W_{\text{air}}$ is the weight of the substance in air • $W_{\text{water}}$ is the weight of the substance when fully immersed in water These formulas allow for the calculation of relative density based on different measurable properties.