Lactometers (used to determine the purity of a sample of milk) and hydrometers (used to determine the density of liquids) are based on the ______ principle.

Archimedes

The correct answer is option 2. Archimedes.

Lactometers and hydrometers are both devices used to measure properties of liquids, such as the density or specific gravity. They operate on the principle of buoyancy, which was famously discovered by the ancient Greek mathematician and scientist, Archimedes.

Archimedes' principle states that when an object is immersed in a fluid, it experiences an upward force called the buoyant force, which is equal to the weight of the fluid displaced by the object. This principle is fundamental to understanding the behavior of objects in fluids, particularly in determining whether they float, sink, or remain suspended.

Lactometers are instruments used to determine the purity of a sample of milk by measuring its specific gravity. A lactometer typically consists of a narrow glass tube with a weighted bulb at one end and a scale on the other. When the lactometer is placed in a sample of milk, it floats at a certain level depending on the density of the milk. The higher the purity of the milk (less diluted with water or other substances), the higher it will float on the scale.

Hydrometers, on the other hand, are devices used to measure the density of liquids. They work on the same principle as lactometers, utilizing buoyancy to determine the specific gravity of a liquid. A hydrometer typically consists of a weighted glass bulb with a graduated stem. When the hydrometer is placed in a liquid, it sinks to a certain level depending on the density of the liquid. The scale on the stem allows for the direct reading of the liquid's specific gravity.

In both cases, the principle of buoyancy, as elucidated by Archimedes, underpins the operation of these instruments. By measuring the displacement of fluid or the buoyant force acting on the device, lactometers and hydrometers provide valuable information about the density and purity of liquids.