UNITS AND MEASUREMENT - NCERT

1 CHAPTER TWOUNITS AND INTRODUCTIONM easurement of any physical quantity involves comparisonwith a certain basic, arbitrarily chosen, internationallyaccepted reference standard called unit. The result of ameasurement of a physical quantity is expressed by anumber (or numerical measure) accompanied by a the number of physical quantities appears to bevery large, we need only a limited number of UNITS forexpressing all the physical quantities, since they are inter-related with one another. The UNITS for the fundamental orbase quantities are called fundamental or base UNITS . Theunits of all other physical quantities can be expressed ascombinations of the base UNITS . Such UNITS obtained for thederived quantities are called derived UNITS . A complete setof these UNITS , both the base UNITS and derived UNITS , isknown as the system of THE INTERNATIONAL SYSTEM OF UNITSIn earlier time scientists of different countries were usingdifferent systems of UNITS for MEASUREMENT .

2 Three suchsystems, the CGS, the FPS (or British) system and the MKSsystem were in use extensively till base UNITS for length, mass and time in these systemswere as follows : In CGS system they were centimetre, gram and secondrespectively. In FPS system they were foot, pound and secondrespectively. In MKS system they were metre, kilogram and system of UNITS which is at present internationallyaccepted for MEASUREMENT is the Syst me Internationaled Unites (French for International System of UNITS ),abbreviated as SI. The SI, with standard scheme of symbols, UNITS and abbreviations, was developed and recommendedby General Conference on Weights and Measures in 1971 international system of of of , precision ofinstruments and errors of formulae anddimensional analysis and itsapplicationsSummaryExercisesAdditiona l exercisesinternational usage in scientific, technical,industrial and commercial work.

3 Because SIunits used decimal system, conversions withinthe system are quite simple and convenient. Weshall follow the SI UNITS in this SI, there are seven base UNITS as given inTable Besides the seven base UNITS , thereare two more UNITS that are defined for (a) planeangle d as the ratio of length of arc ds to theradius r and (b) solid angle d as the ratio ofthe intercepted area dA of the spherical surface,described about the apex O as the centre, tothe square of its radius r, as shown in Fig. (a)and (b) respectively. The unit for plane angle isradian with the symbol rad and the unit for thesolid angle is steradian with the symbol sr. Boththese are dimensionless SI Base Quantities and UNITS * UNITS AND MEASUREMENT17*The values mentioned here need not be remembered or asked in a test. They are given here only to indicate theextent of accuracy to which they are measured.

4 With progress in technology, the measuring techniques getimproved leading to measurements with greater precision. The definitions of base UNITS are revised to keep upwith this progress.(a)(b)Fig. of (a) plane angle d and(b) solid angle d .BaseSI UnitsquantityNameSymbolDefinitionLengthm etremThe metre is the length of the path travelled by light in vacuumduring a time interval of 1/299,792,458 of a second. (1983)MasskilogramkgThe kilogram is equal to the mass of the international prototypeof the kilogram (a platinum-iridium alloy cylinder) kept atinternational Bureau of Weights and Measures, at Sevres, nearParis, France. (1889)TimesecondsThe second is the duration of 9,192,631,770 periods of theradiation corresponding to the transition between the twohyperfine levels of the ground state of the cesium-133 atom.(1967)ElectricampereAThe ampere is that constant current which, if maintained incurrenttwo straight parallel conductors of infinite length, of negligiblecircular cross-section, and placed 1 metre apart in vacuum,would produce between these conductors a force equal to 2 10 7newton per metre of length.

5 (1948)ThermokelvinKThe kelvin, is the fraction 1 of the thermodynamicdynamictemperature of the triple point of water. (1967)TemperatureAmount ofmolemolThe mole is the amount of substance of a system, which containssubstanceas many elementary entities as there are atoms in of carbon - 12. (1971)LuminouscandelacdThe candela is the luminous intensity, in a givenintensitydirection, of a source that emits monochromatic radiation offrequency 540 1012 hertz and that has a radiant intensity inthat direction of 1/683 watt per steradian. (1979)PHYSICS18 Table Some UNITS retained for general use (Though outside SI)Note that when mole is used, the elementaryentities must be specified. These entitiesmay be atoms, molecules, ions, electrons,other particles or specified groups of employ UNITS for some physical quantitiesthat can be derived from the seven base UNITS (Appendix A 6).

6 Some derived UNITS in terms ofthe SI base UNITS are given in (Appendix A ).Some SI derived UNITS are given special names(Appendix A ) and some derived SI UNITS makeuse of these UNITS with special names and theseven base UNITS (Appendix A ). These aregiven in Appendix A and A for your readyreference. Other UNITS retained for general useare given in Table SI prefixes and symbols for multiplesand sub-multiples are given in Appendix guidelines for using symbols for physicalquantities, chemical elements and nuclides aregiven in Appendix A7 and those for SI UNITS andsome other UNITS are given in Appendix A8 foryour guidance and ready MEASUREMENT OF LENGTHYou are already familiar with some direct methodsfor the MEASUREMENT of length. For example, ametre scale is used for lengths from 10 3 m to 102m. A vernier callipers is used for lengths to anaccuracy of 10 4 m.

7 A screw gauge and aspherometer can be used to measure lengths asless as to 10 5 m. To measure lengths beyond theseranges, we make use of some special MEASUREMENT of Large DistancesLarge distances such as the distance of a planetor a star from the earth cannot be measureddirectly with a metre scale. An important methodin such cases is the parallax you hold a pencil in front of you againstsome specific point on the background (a wall)and look at the pencil first through your left eyeA (closing the right eye) and then look at thepencil through your right eye B (closing the lefteye), you would notice that the position of thepencil seems to change with respect to the pointon the wall. This is called parallax. Thedistance between the two points of observationis called the basis. In this example, the basis isthe distance between the measure the distance D of a far awayplanet S by the parallax method, we observe itfrom two different positions (observatories) A andB on the Earth, separated by distance AB = bat the same time as shown in Fig.

8 Wemeasure the angle between the two directionsalong which the planet is viewed at these twopoints. The ASB in Fig. represented bysymbol is called the parallax angle orparallactic the planet is very far away, 1,bD<< andtherefore, is very small. Then weapproximately take AB as an arc of length b of acircle with centre at S and the distance D asUNITS AND MEASUREMENT19ttttthe radius AS = BS so that AB = b = D where is in radians. D = b ( )Having determined D, we can employ a similarmethod to determine the size or angular diameterof the planet. If d is the diameter of the planetand the angular size of the planet (the anglesubtended by d at the earth), we have = d/D( )The angle can be measured from the samelocation on the earth. It is the angle betweenthe two directions when two diametricallyopposite points of the planet are viewed throughthe telescope.

9 Since D is known, the diameter dof the planet can be determined using Eq. ( ).Example Calculate the angle of(a) 10 (degree) (b) 1 (minute of arc or arcmin)and (c) 1 (second of arc or arc second) inradians. Use 3600=2 rad, 10=60 and1 = 60 Answer (a) We have 3600 = 2 rad10 = ( /180) rad = 10 2 rad(b)10 = 60 = 10 2 rad1 = 10 4 rad 10 4 rad(c)1 = 60 = 10 4 rad1 = 10 4 rad 10 6 radtExample A man wishes to estimatethe distance of a nearby tower from stands at a point A in front of the towerC and spots a very distant object O in linewith AC. He then walks perpendicular toAC up to B, a distance of 100 m, and looksat O and C again. Since O is very distant,the direction BO is practically the same asAO; but he finds the line of sight of C shiftedfrom the original line of sight by an angle = 400 ( is known as parallax ) estimatethe distance of the tower C from his originalposition We have, parallax angle = 400 From Fig.

10 , AB = AC tan AC = AB/tan = 100 m/tan 400= 100 = 119 mtExample The moon is observed fromtwo diametrically opposite points A and Bon Earth. The angle subtended at themoon by the two directions of observationis 1o 54 . Given the diameter of the Earth tobe about 107 m, compute thedistance of the moon from the We have = 1 54 = 114 ()()-6114 10= rad= 102rad,since 61 "rad Also b=AB= 107 Hence from Eq. ( ), we have the earth-moondistance,D b=/ = 7-2 10 m= tExample The Sun s angular diameteris measured to be 1920 . The distance D ofthe Sun from the Earth is 1011 is the diameter of the Sun ?Fig. Parallax Sun s angular diameter =1920" = = s diameter dD= 10m = 9= 10 m of Very Small Distances:Size of a MoleculeTo measure a very small size like that of amolecule (10 8 m to 10 10 m), we have to adoptspecial methods.