Physics | Units and Measurements part 4 | for competitive exams

Mass density or density :

→ $\mathrm{Density}=\frac{\mathrm{Mass}}{\mathrm{Volume}}$ (or)

$\mathrm{Density(\rho )}=\frac{M}{V}$

→ If mass is constant, density is inversely proportional to volume.

$\rho \propto \frac{1}{V}$

If the volume increases, then density decreases.

If the volume decreases, then density increases.

→ If the volume is constant, density is directly proportional to mass.

ρ ∝ M

If the mass increases, then density increases.

If the mass decreases, then density decreases.

→ SI unit of mass density is kg/m³.

→ CGS unit of mass density is gram per cubic centimeter.

→ The unit of density in FPS (Foot Pound System) is lb/ft³.

→ The dimensional formula of mass density is M L^-3 T⁰.

→ 1 gram/cm³ = 1000 kg/m³.

→ The value of density of water at 4°C (or 277 K) is 1 gm/cm³ or 1000 kg/m³.

→ Density of water is maximum at 4°C (or 277 K).

→ Density of water decreases when it freezes below 4°C.

→ When water is heated from 0°C to 4°C, its density increases.

→ The volume of a given amount of water decreases when its temperature is increased from 0°C to 4°C.

→ The density of fresh water is less than the density of salt water because when salt is added to the fresh water, the mass of the water increases. So the density of the water increases. So salt water has more density than fresh water.

→ Density of ice is less compared to density of water.

→ Ice density is less than water. So ice floats on water.

→ Aerographene is the least dense solid known on earth. Its density is 160 g/m³.

→ The densest stable element known on Earth is osmium, with a density of approximately 22.59 g/cm³.

→ The average density of the Earth is approximately 5.513 g/cm³ or 5,513 kg/m³.

→ The density of steel ranges between 7.75 and 8.05 g/cm³.

→ The density of mild steel ranges from 7,800 to 7,870 kg/m³ or 7.8 to 7.87 g/cm³.

→ Mercury is the densest liquid at standard room temperature and pressure.

→ A steel ball floats on mercury because the density of mercury is higher than that of steel.

→ An object float on a liquid when the density of the object is less than that of the liquid.

Densities of some important substances:

S. No.	Substance	Density (g/cm3)	Density (kg/m3)
1.	Air		1.225
2.	Saturn(planet)	0.687	687
3.	Ice	0.917	917
4.	Water	1	1000
5.	Aluminium	2.71	2710
6.	Diamond	3.51
7.	Earth(planet)	5.513	5,513
8.	Copper	8.96	8,960
9.	Silver	10.49	10,490
10.	Lead	11.34	11,340
11.	Mercury	13.6	13,600
12.	Tungsten	19.25	19,250
13.	Gold	19.32	19,320
14.	Platinum	21.45	21,450

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Relative density (or specific gravity):

→ $\mathrm{Relative\; density}=\frac{\mathrm{density\; of\; a\; substance}}{\mathrm{density\; of\; water}}$

→ Relative density of a substance has no unit.

→ Relative density has no dimensions.

→ The dimensional formula for specific gravity is M⁰ L⁰ T⁰.

→ Relative density is also known as specific gravity.

→ The instrument used to find the relative density of liquids is hydrometer.

→ A density bottle is also known as a pycnometer or specific gravity bottle is used to determine water content and specific gravity.

→ The specific gravity of water at standard atmospheric conditions is 1.

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