WWm l 2006 -071 m I URGETIIT 2006-07 ARIHANTPRAKASHAN KALI NDI ,T.RNAGAR,MEERUT- 2 5 00 0 2 y^jdhanic" p -_atoB "ei EEE PHYSICS D.B.SI NGH Director VigyanGurkui,KOTA Ot herUsefulBooks "7extS4F = ma TTrAz'mAs Stepn - * F= m -=- -kilogram xmetre StepIIIF =r rsecond xsecond StepIV>Theunitofforce 2 =kilogrammetrepersecond 4.Abbreviationsformultiplesandsubmultiples: FactorPrefixSymbol 1024 yottaY 1021 zettaZ 1018 exaE 1015 petaP 1012 teraT 109 g' gaG 106 megaM 103 kilok 102 hectoh 101 dekada 10-1 decid ur2 centicm 10"3 millim 10"6 micro M 10"9 nanon 10"12 pico P io-15 femtof 8UnitsandMeasurements FactorPrefix 10-18 atto 10-21 zepto 10-24 yocto 106 million 109 billion 1012 trillion Symbol a z y 5.Someapproximatelengths: MeasurementLengthinmetres Distancetothefirstgalaxiesformed2 x1026 on DistancetotheAndromedagalaxy2 x10 Distancetotheneareststar.4X1016 (ProximaCentauri) DistanceofPluto6X1012 RadiusofEarth6 x106 HeightofMountEverest9 x103 Thicknessofthispage1 x10_4 Lengthofatypicalvirus1 x10"8 Radiusofahydrogenatom5 x10711 Radiusofaproton1 X 10~ 6.Someapproximatetimeintervals: Measurement 1 5 Timeinterval insecond 1x l O ' ,39 5 x1017 11 1 x1 0 2 x l 09 9x104 -1 Lifetimeofaproton(predicted) Ageoftheuniverse Ageofthepyramidofcheops Humanlifeexpectancy Lengthofaday Timebetweenhumanheartbeats LifetimeoftheMuon Shortestlablightpulse Lifetimeofthemostunstableparticle ThePlanktime 7.Someapproximatemasses: ObjectMassinkilogram 8 x 1 0 2x10" 6 6 x 1 0 1 x1 0 1 x1 0 R 1 5 I - 2 3 , - 4 3 Knownuniverse Ourgalaxy Sun Moon AsteroidEros Smallmountain Oceanliner Elephant Grape Speckofdust Penicillinmolecule Uraniumatom Proton Electron 1 x10M 2 x1041 2 x1030 7 x1022 5 x1015 1 x1012 7 x107 5 x l 03 3 x10~3 7 x 1 0 5 x10 4 x 1 0 2 x 1 0 9 x 1 0 -10 - 17 - 25 - 27 - 31 8.DimensionsandDimensionalFormulae:The dimensionsofaphysicalquantityarepowersraised to fundamentalunitstogetthederivedunitofthatphysical quantity.Thecorrespondingexpressionisknownas dimensionalformula. Inthe representationofdimensionalformulae,fundamental quantitiesarerepresentedbyonelettersymbols. FundamentalQuantitySymbol MassM LengthorDistanceL TimeT ElectriccurrentI TemperatureK Amountofsubstancemol Luminousintensitycd Methodforfindingdimensionalformulae: StepI :Writetheformulaofphysicalquantity. StepI I :Converttheformulainfundamentalphysical quantity. StepI I I :Writethecorrespondingsymbolforfundamental quantities. StepI V:Makeproperalgebraiccombinationandget theresult. Example:Findthedimensionsofmomentum. Solution:StepIMomentum= MassxVelocity StepII>Momentum= Massx Displacement Time StepIII>Momentum= _MA IT] Dimensionalformulaofmomentum =[Momentum] =[MLT- 1] Thedimensionsofmomentumare1inmass,1 inlength and-1intime. Example:TheunitofgravitationalconstantisNm/kg. Finddimensionsof gravitationalconstant. Solution:StepI>Writephysicalquantitiesofcorres-pondingunits. Nm2Force(Length)2 Here,=- =5 kg2(Mass)2 StepII>Convertderivedphysicalquantitiesin fundamentalquantities. Gravitationalconstant= Force x(Length) (Mass)2 (Mass x Acceleration)x(Length) Mass (Mass)2 (Length)' (Mass) Changeinvelocity Time /Distance ^ (Length)2 Mass xTimeTime StepIII>Usepropersymbolsoffundamentalquantities. Gravitationalconstant= [L2][L] 9UnitsandMeasurements =[Gravitational constant] = MTT [MT][T] ..Thedimensionalformulaofgravitationalconstant 9.UnitandDimensionsofsomePhysicalQuantities =[M~1L3T~2] s. NameofSIUnitSIUnits Dimensional No. PhysicalQuantityFormulaNameofSIUnitSIUnits Formula 1.Displacementordistance orlength length metre m ML1T 2.Mass kilogram kgM W 3.Timeseconds ML T1 4.Electriccurrent ampereA M L T 5.Thermodynamickelvin K temperature K 6.Amountofmole mol substance mol 7.Luminousintensit" J candelacd 8.Area lengthxbreadth squaremetre m2 ML2T 9.Volumelengthxbreadth xheight cubicmetre m3 ML3T 10.Densitymasskilogrampercubic kg/m3 M1L"3T Density volumemetre kg/m3 M1L"3T 11.Relativedensityorspecificdensityofsubstance kg/m3 MLT0or dimensionless gravity densityof water at4C kg/m3 MLT0or dimensionless = nounit 12.Velocityorspeeddistancemetrepersecond m/sML1T_ 1 time m/sML1T_ 1 13.Accelerationor retardationorg changeinvelocity time metrepersquaresecond m/s2 MV T -2 14.Force(F)massxaccelerationnewtonor kilogrammetreper Norkgm/sM1L1T- 2 squaresecond 15.Linearmomentum(p)massxvelocitykilogrammetreper second kgm/sM V T- 1 16.Impulse force xtimeintervalnewton-secNs M V T- 1 17.Pressureforcepascalornewtonper N/m2orPa M1L_1t - 2 areasquaremetre N/m2orPa 18.Workforcexdistancekilogram-squaremetre persquaresecondor kg-m/sorJMV T- 2 joule kg-m/sorJ 19.Energyequivalenttoworkkilogramsquaremetre kgm2/s2 orJ M1L2T- 2 persquaresecondor kgm2/s2 orJ M1L2T- 2 joule kgm2/s2 orJ 20.Power(P)workwatt(W)orjouleper timesecondorkilogram kgm2/s3orJ/s M1L2T- 3 squaremetrepercubic orwatt(W) M1L2T- 3 second 21.Gravitationalconstant(G) mim2 newton-squaremetre persquarekilogram Nm2/kg2 M - 1 L 3 T - 2 arc rad MLTor 22.Angle(8) arc radianrad MLTor 22.Angle(8) radius radianrad dimensionless 23.Angularvelocity(co)angle(9)radianpersecond rad/sM0LT_ 1 Angularvelocity(co) time radianpersecond rad/sM0LT_ 1 5UnitsandMeasurements PhysicalQuantityFormulaNameofSIUnitSIUnits Dimensional Formula Angularacceleration(a) Momentofinertia(J) Radiusofgyration(K) Angularmomentum(L) Torque( ? ) (Spring)forceconstant(k) Surfacetension Surfaceenergy Stress Strain Young'smodulus(Y) Bulkmodulus(B) Compressibility Modulusofrigidityor shearmodulus Coefficientofviscosity(r|) Coefficientofelasticity Reynold'snumber(R) Wavelength(X) Frequency(v) Angularfrequency(co) Timeperiod Intensityofwave(I) Gasconstant(R) Velocitygradient changeinangular velocity timetaken mass x(distance)2 distance Z? force displacement force length energy area force area changeindimenson originaldimension AL L logitudinalstress logitudinalstrain volumes tress volumestrain or or normalstress volumestrain V1 _7 Bulkmodulus shearings tress shearingstrain F 11=/.^ Au AT ~ Ax stress strain prVc 11 distance numberof vibrations second co = 2TU> I=ln2n2a2pvorenergy transportedperunit areapersecond PV nT velocitychange distance radianpersquare second kilogramsquaremetre metre kilogramsquaremetre persecond newtonmetreor kilogram-squaremetrepersquare second newtonper metreorkilogramper squaresecond newtonpermetre joulepermetresquare newtonpersquare metre Nounit newtonpersquare metre newtonpersquare metre squaremetreper newton newtonpersquare metre poiseorkilogramper metrepersecond newtonpersquare metre nounit metre persecondorhertz radianpersecond second wattpersquaremetre joulepermolekelvin persecond rad/s kgm2 m kgm2/s N-morkgm2/s2 N/morkg/s N/m J/m2 N/m2 N/m N/m N_ 1m2 N/m kgm*s1orpoise N/m m s"1orHz rad/s s W/M Jmol- 1K"1 MLT-M1L2T M ^ T0 MVT- 1 M1L2T~2 M1LT~2 M1L T- 2 M ^ T -2 M1L- 1T- 2 MLT M' l ^ T- 2 I VT VT2 M 1 L - 1t - 2 M^^T-1 m i l - I t - 2 MLT MVT0 MVT-1 m V T -1 M W m V T "3 M1L2T_ 2K_ 1 M0L0T_ 1 6UnitsandMeasurements S. No. PhysicalQuantityFormulaNameofSIUnitSIUnits Dimensional Formula 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. Rateofflow Thermalconductivity(K) Specificheat(c) Latentheat(L) Planck'sconstant(h) Boltzmannconstant(fc/j) Stefan'sBoltzmann constant(a) Charge Dielectricconstant Electricfield Potential(electric) Electricdipolemoment Resistance(R) Electricflux (0or E) Permittivityoffreespace (E0) Capacitance Specificresistanceor electricalresistivity Conductance Currentdensity EMF(E) Magneticfield(B) Permeabilityoffreespace (Mo) Magneticdipolemoment (M) Magneticflux Inductance (LorM) Timeconstant orCR volumeflow K time Q c~ Q ?ti At Q rn energy frequency PV TNA E AtT" q = It K FFAV E = orE = qa V: W 1 p =2qL r-7 C3 (b)C1 = C2 = C3 (c)C!