2.2 The international system of units - Units and Measurements - class 11 Physics
2.2 THE INTERNATIONAL SYSTEM OF UNITS
Accessible NCERT Class 11 Physics books by Dr T K Bansal.
In earlier time scientists of different countries were using different systems of units for measurement. Three such systems,
the CGS,
the FPS (or British) system and
the MKS system
were in use extensively till recently.
The base units for length, mass and time in these systems were as follows :
• In CGS system they were centimetre, gram and second respectively.
• In FPS system they were foot, pound and second respectively.
• In MKS system they were metre, kilogram and second respectively.
The system of units which is at present internationally accepted for measurement is the Systeme International d’ Unites (French for International System of Units), abbreviated as SI. The SI, with standard scheme of symbols, units and abbreviations, was developed and recommended by General Conference on Weights and Measures in 1971 for international usage in scientific, technical, industrial and commercial work. Because SI units used decimal system, conversions within the system is quite simple and convenient. We shall follow the SI units throughout in this book.
In SI, there are seven base units as given in Table 2.1.
Table 2.1 SI Base Quantities, Units, symbols and definition*
[* The values or definitions mentioned here need not be remembered or asked in a test. They are given here only to indicate the extent of accuracy to which they are measured. With progress in technology, the measuring techniques get improved leading to measurements with greater precision. The definitions of base units are revised to keep up with this progress.]
| Base quantity | Unit | Symbol | Definition | |
|---|---|---|---|---|
| Length | Metre | M | The metre is the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second. (1983) | |
| Mass | Kilogram | Kg | The kilogram is equal to the mass of the international prototype of the kilogram (a platinum-iridium alloy cylinder) kept at international Bureau of Weights and Measures, at Sevres, near Paris, France. (1889) | |
| Time | Second | s | The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom. (1967) | |
| Electric current | ampere | A | The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to 2×10−7 newton per metre of length. (1948) | |
| Thermodynamic Temperature | Kelvin | K | The kelvin, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. (1967) | |
| Amount of substance | Mole | Mol | The mole is the amount of substance of a system, which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon - 12. (1971) | |
| Luminous Intensity | Candela | cd | The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian. (1979) |
Besides the seven base units, there are two more units that are defined for (a) plane ∠ dθ as the ratio of length of arc ds to the radius r and (b) solid ∠ dω as the ratio of the intercepted area dA of the spherical surface, described about the apex O as the centre, to the square of its radius r, as shown in Fig. 2.1(a) and (b) respectively. The unit for plane angle is radian with the symbol rad and the unit for the solid angle is steradian with the symbol sr. Both of these are dimensionless quantities.
Fig 2.1a description of plane ∠ d theta and (b) solid ∠ d omega
Fig 2.1b description of solid ∠ d omega
Note that when mole is used, the elementary entities must be specified. These entities may be atoms, molecules, ions, electrons, other particles or specified groups of such particles.
We employ units for some physical quantities that can be derived from the seven base units (Appendix A 6). Some derived units in terms of the SI base units are given in (Appendix A 6.1). Some SI derived units are given special names (Appendix A 6.2 ) and some derived SI units make use of these units with special names and the seven base units (Appendix A 6.3). These are given in Appendix A 6.2 and A 6.3 for your ready reference. Other units retained for general use are given in Table 2.2.
Table 2.2 Some units are retained for general use (Though outside SI)
| Name | Unit of | Symbol | Value in the SI unit |
|---|---|---|---|
| Minute | Time | Mm | 60 s |
| Hour | Time | H | 60 mm = 3600 s |
| Day | Time | D | 24 h = 86400 s |
| Year | Time | Y | 365.25 d = 3.156 × 10^7 s |
| Tone | Mass | T | 10^3 kg |
| Quintal | Mass | q | 100 kg |
| Carat | Mass | C | 200 mg |
| Degree | Plane angle | ° | 1° = (π/ 180) rad |
| Litre | Volume | L | 1 dm^3 = 10^−3 m^3 |
| Bar | Pressure | bar | 0.1MPa=10^5Pa |
| standard atmospheric pressure | Pressure | Atm | 101325 Pa = 1.013 × 10^5 Pa |
| Curie | Radio activity | Ci | 3.7 x 10^10 s−1 |
| Roentgen | R | 2.58 × 10^−4 C/kg | |
| Barn | b | 100 fm^2= 10^2m^2 | |
| Are | Area | a | 1 dam^2 = 10^2 m^2 |
| Hectare | Area | ha | 1 hm^2 = 10^4 m^2 |
Common SI prefixes and symbols for multiples and sub-multiples are given in Appendix A2. General guidelines for using symbols for physical quantities, chemical elements and nuclides are given in Appendix A7 and those for SI units and some other units are given in Appendix A8 for your guidance and ready reference.