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The concept of buoyant force plays a central role in understanding why objects appear lighter in a fluid than in air. Archimedes' Principle states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. In simpler terms, when an object is placed in water or any other fluid, there is an upward force exerted by the fluid on the object.
This upward force is what makes objects feel lighter when submerged. In the case of the iron anchor, the buoyant force is 210 N, which means the water is pushing up on the anchor with a force equivalent to the weight of 210 N. This is why its "apparent" weight in water is less than its actual weight in air.

Density is a property of matter that describes how much mass is contained in a given volume. It is mathematically expressed by the formula \( \rho = \frac{m}{V} \), where \( \rho \) is the density, \( m \) is the mass, and \( V \) is the volume.
For the iron anchor, the density is given as 7870 kg/m³. This indicates that each cubic meter of iron has a mass of 7870 kilograms. When considering buoyant force, the density of the fluid (in this case, water) is equally important. Freshwater has a density of 1000 kg/m³, which is why it can exert a buoyant force strong enough to make dense materials like iron appear lighter when submerged.

A submerged object is one that is fully or partially sunk in a fluid, such as water. The behavior of a submerged object underlies the principles explored in this exercise. When the iron anchor is submerged, it displaces a volume of water equal to its own volume.
According to Archimedes’ Principle, the displaced water's weight is responsible for the buoyant force experienced by the object. The submerged anchor exemplifies this principle, appearing lighter because the fluid it displaces (water) exerts an upward force matching the weight of the displaced water. This interaction helps determine the volume of the anchor by reversing the displacement process.

Weight measurement of an object can vary depending on whether it is measured in air or when submerged in a fluid. In air, an object's weight is simply the force of gravity acting on it, calculated as \( W = mg \), where \( m \) is the mass and \( g \) is the gravitational acceleration (9.8 m/s² on Earth).
However, when submerged, the object seems lighter due to the buoyant force acting upwards. For the anchor, its weight in air is calculated using its density, volume, and gravity \( W_{\text{air}} = \rho_{\text{iron}} \times V_{\text{anchor}} \times g \). By knowing the anchor feels 210 N lighter in water, its real weight can be pinpointed to approximately 1646.89 N in air. Such calculations emphasize the importance of taking fluid effects into account for accurate weight assessments in different environments.