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Specific gravity, often abbreviated as SG, is a dimensionless quantity that represents the ratio of the density of a substance to the density of a reference substance. In most cases, for liquids and solids, the reference substance is water at a temperature of 4°C, where it has maximum density. An SG value tells us how heavy a substance is compared to water, without regard to the actual units of measurement.
For example, the specific gravity of wood in our problem is 0.50. This means the wood's density is half that of water. Because the specific gravity is less than 1, the wood will float. However, only half of its volume will be submerged when it is floating naturally in water.
This concept is useful in buoyancy calculations, as it helps predict whether an object will float or sink when placed in a fluid. It acts as a comparative tool, simplifying density-related problems by reducing them to ratios.

The density (\( \rho \) ) of a substance is a measure of how much mass is packed into a given volume. It is usually expressed in kilograms per cubic meter (kg/m³) or grams per cubic centimeter (g/cm³). The formula for density is \( \rho = \frac{m}{V} \), where \( m \) is mass and \( V \) is volume.
Understanding the density of a substance allows you to calculate its specific gravity or determine its behavior when immersed in a fluid. In this exercise, the wood has a density of 500 kg/m³, calculated by multiplying its specific gravity (0.50) by the density of water (1000 kg/m³).
Different substances have distinct densities, which influence how they interact with each other in terms of floating and sinking. Knowing the density helps solve buoyancy problems, as it provides insights into how much of a substance will be submerged when in water or any other fluid, and how much force is required to make it entirely sink.

Archimedes' principle is a fundamental law of physics that describes how buoyancy works. According to this principle, any object fully or partially submerged in a fluid experiences a buoyant force equal to the weight of the fluid displaced by the object.
This concept is key to understanding why and how objects float. When you place an object in a fluid, like water, it pushes some of the fluid out of the way. The fluid then pushes back up against the object with a force equivalent to the weight of the displaced fluid.
In the exercise, the wooden block initially floats because the buoyant force perfectly balances the weight of the wood. When the lead is attached, it increases the weight, making it necessary for a larger volume of water to be displaced to maintain buoyancy. Eventually, the additional weight from the lead tips the balance, causing the combined weight of the wood and lead to match the buoyant force from the fully displaced water, leading to submersion.