Archimedes Principle | Science & Technology for UPSC CSE PDF Download

When a body is partially or wholly immersed in a fluid at rest, it seems to lose a part of its weight which is equal to the weight of the fluid displaced.

Specific Gravity. It is the ratio of the weight of any volume of substance to the weight of an equal volume of water at 4° C. It being a ratio is a pure number and this has no units. Specific gravity is sometimes called relative density.

Density and Specific Gravity

(i) Density is mass per unit volume of a substance whereas sp. gr. is the ratio of the density of a substance to the density of water at 4° C.

(ii) Density is expressed in units whereas specific gravity has no units.

Hydrometers. These are the instruments used to find the specific gravity of liquids quickly and directly without calculations. They work on the principle of floatation. These are of two types.

(i) Constant weight but variable immersion instruments e.g., common hydrometer, Beaume’s hydrometer, Tweddlell’s hydrometer and lactometer.

(ii) Variable weight but constant immersion in struments e.g., Nicholson’s hydrometer.

Lactometer. It is used for testing milk adulteration with water. Markings on the stem indicate the water- milk ratio. The instrument is not very reliable for testing of purity.
If cream is taken out of milk, the skimmed milk has higher density because cream is higher constituent.

Nicholson’s Hydrometer. The instrument can be used to find density of solids as well as liquids.

Law of Floatation The law of floatation states: A floating body displaces its own weight of the fluid in which it floats.
Archimedes’ principle and law of floatation can explain several phenomena. An iron nail sinks in water whereas a ship made of iron and steel floats. This is due to the fact that a ship is hollow and contains air and, therefore, its density is less than that of water. A ship sinks in water to a level such that the weight of the displaced water equals its own weight. Since the density of sea water is more than that of river water, a ship sinks less in sea water. It is for this reason that a ship rises a little when it enters a sea from a river. It is because of the higher density of sea water that it is easier to swim in the sea.

A submarine has large ballast tanks. When these tanks are filled with water the average density of the submarine becomes more than that of water and it can dive easily. When the submarine is ready to surface, compressed air is forced into the ballast tanks forcing the water out, thus reducing the density of the submarine, which can then rise.
A solid chunk of iron will sink in the water but float in mercury because the density of iron is more than that of water but less than that of mercury.

A balloon filled with a light gas, such as hydrogen, rises because the average density of the balloon and the gas is less than that of air. The balloon cannot rise indefinitely because the density of the air decreases with increasing altitude. At a certain height, where the density of air is equal to the average density of the balloon, it ceases to rise and drifts sideways with the wind.

Ice, being less dense than water, floats in it with one tenth of its volume above the surface. When ice melts it contracts by as much of its volume as was above the surface and, therefore, the level of water remains unchanged.