## Summary

One of the most useful discoveries to mankind in the field of physics is Archimedes’ principle. Based on this principle, a device called a hydrometer was developed which helps in measuring the density of liquids with ease.

Archimedes’ principle states that “When a body is immersed completely or partially in a fluid, it experiences an upward force that is equal to the weight of the fluid displaced by the body.”

According to the principle, a solid that floats or is immersed in a liquid appears to lose its weight which is equal to the weight of the liquid displaced by the solid. Whether a given solid drowns or not in a given liquid depends on the density of the solid in comparison with that of the liquid.

For an easy approach, we consider the relative density of the substance, which is the ratio of the density of the substance to the density of water, which obviously has no units but a mere number.

If the relative density of the given solid is greater than that of the given liquid, it drowns in the liquid as there is a net downward force on the solid after it gets completely immersed in the liquid. If the relative density of the liquid and that of the solid are equal, then the solid just floats or drowns.

This implies that the solid immerses in the given liquid and stays suspended at the kept position. If the relative density of the given solid is lesser than that of the given liquid, it floats in the liquid.

This happens due to the up thrust or buoyant force of the liquid acting on the solid. The relative density of a floating solid in a given liquid gives the measure of the percentage of the solid that lies below the surface of the liquid.

The “relative density” or “specific gravity” of a substance is defined as the ratio of its density to the density of water at 4 degrees Celsius.

Relative density = $\frac{\text{Density of substance}}{\text{Density of water at 4}\mathbb{C}}$

This can be expressed in many ways. If the numerator and the denominator are both multiplied by “volume”, then we get the expression relative density is equal to the ratio of “mass of the substance” to “mass of water of the same volume.”

Relative density = $\frac{\text{Mass of substance}}{\text{Mass of water of same volume}}$

Again, when the numerator and the denominator are both multiplied by acceleration due to gravity “g”, the expression becomes:

Relative density = $\frac{\text{Weight of substance}}{\text{Weight of water of same volume}}$

When the substance is immersed in water, it displaces water of volume equal to its own volume. According to Archimedes’ principle, the apparent loss of weight of a body immersed in water is equal to the weight of the water displaced. Therefore:

Relative density = $\frac{\text{Weight of substance}}{\text{Apparent loss of weight when immersed in water}}$

This expression can be used to find the relative density of a solid body. In order to find the relative density of a liquid, a solid body is taken and its weight is found in air. Then, the weight of the same body is found when it is completely immersed in the liquid whose relative density is to be found. Finally, the weight of the body is found by immersing it completely in water.

The relative density of the liquid can be found using the expression:

Relative density = $\frac{\text{Loss of weight of a solid body when immersed in liquid}}{\text{Loss of weight of the same body when immersed in water}}$

- The relative density of a substance is the ratio of density of the substance to the density of water.
- Relative density should be calculated using the same system of units for the substance as well as water.
- A hydrometer uses Archimedes’ principle to determine the density of any liquid.
- Archimedes’ principle is also used in designing ships and submarines.