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Physics Measurements Notes for JEE Main 2015 by ednexa.com

- 1. 9011041155 / 90110311551Measurements Physics Physics is a branch of science which deals with study of natural phenomenon of non-living things. Origin fusesPhysical quantitiesThe quantities which can be measured with physical apparatus or physical means are called physical quantities. e.g.mass Length

2. 9011041155 / 90110311552Time Temperatureetc.Physical quantities are expressed in terms of magnitude and unit. Non physical quantitiesThe quantities which cannot be measured with physical apparatus or no physical apparatus is available for their measurement are called non-physical quantities.e.g. Intelligence of a person, happiness etc. 3. 9011041155 / 90110311553MeasurementMeasurement of a physical quantity is its careful and accurate comparison with the standard of that quantity. UnitThe standard used for comparison of a physical quantity is called unit of that quantity. e.g. 1kg 4. 9011041155 / 90110311554MagnitudeMagnitude of a physical quantity is the number which indicates how many times the unit is contained in it. e.g. 10 litresThe physical quantities are classified in to two types1. Fundamental quantities :- The physical quantities which can be independently measured and expressed are called fundamental quantities. Thus, these quantities can be measured and expressed without taking help of other quantities. e.g. length, mass, time, temperature etc.Fundamental units :- The units of the fundamental quantities are called fundamental units. 5. 9011041155 / 90110311555e.g. metre, kilogram, second etc. Fundamental quantitiesi. lengthMetre(m)ii. massKilogram(kg)iii. timeSeconds(s)iv. temperatureKelvin(K)v. Electric currentAmpere(A)vi. Luminous IntensityCandela(cd)viii. Amount of substanceMole(mol)Supplementary Quantities i. Plane angle Radian rad ii. Solid Angle Steradian sr 6. 9011041155 / 90110311556iii. Frequency 1/t = 1/s = Hertz (Hz)2. Derived quantities :- The physical quantities which require two or more fundamental quantities for their measurement and expression are called derived quantities.e.g. speed, acceleration, force etc.Derived units :- The units of derived quantities are called derived units.e.g. m/s, m/s2, newton etc.Requirements of good units1. The unit should be easy to use and read.2. Its magnitude should not change with respect to time, temperature, place and observer.3. It should be easily reproducible. It means, it should be easy to copy and can be produced anywhere any quantity. 4. It should be acceptable worldwide. 7. 9011041155 / 90110311557(universally acceptable ) System of unitsThe fundamental units together with all derived units form a system of units. Formerly there were different unit systems used in different countries. Some of the most common unit systems were as follows :- 1. C.G.S. 2. M.K.S. 3. F.P.S.4. S.I.( System International ) :- To avoid difficulties in inter conversions of units and to have uniformityin the units used all over the world, General Conference of weights and Measures suggested animproved metric system called System International in 1960. It was accepted by I.S.O.( InternationalStandards Organization ) in 1962. This includes all the fundamental units from M.K.S. and over 450 8. 9011041155 / 90110311558derived units. As far as possible the units are named after renowned scientists to honour them.Before the introduction of S.I. exchange of information between the scientists of differentcountries was difficult because of the difference between the unit systems used by them. With the worldwide use of S.I. this difficulty is removed.Now in this common language of units, scientists engineers and technicians all over the world can exchange their ideas, criticism easily. So, this system has bridged-up the gap between them.Rules of writing S.I. units1. metre, joule, newtonMetre, Joule,Newton 9. 9011041155 / 901103115592. cm, m/s, J, NCm, M/s, j, n etc. 3. singular form only. plural form of units:- not allowed, e.g. While speaking, we may say that the mass is 100 kilograms,but while writing, we should write 10kg only and not 10kgs. 4. No punctuation markse.g. the unit newton metre should be written as Nm and not like N-m or N,m etc. m/s is a valid unit because the slash (/) is not a punctuation mark. It is a mathematical operator. 10. 9011041155 / 901103115510DimensionsIncreasing the power of fundamental units to find outunits of derived quantities is known as dimensions.1.0 1 1displacementVelocityTimeVT[ M L T ] m / s l2. Area = 2= [ M0 L2 T0] = m23. Volume = 3= [ M0L3T0] = m3 11. 9011041155 / 9011031155114.20 1 2 2V / TAccelerationT TTM LT m / s ll5. Force = ma= m / T2= [ M1L1T-2] = kg m / s2 = N6. Work = F . = ma . = m . / T2 . = m . 2 / T2= [ M1 L2 T-2] = kg . m / s2 = J 12. 9011041155 / 9011031155127.222 21 1 2 2ForcePr essureAreamam. / T m.TM L T kg m / s lll l8.221 2 3 2 33WorkPowerTimeF .Tma .Tm . / T .TmM L T kgm / s wT lll ll 13. 9011041155 / 9011031155139. P.E = mgh21 2 2 2 2m. / T .M L T kgm / s J l l10.22 21 2 2 2 21K.E mv21m. / t2[M L T ] kgm / s J l11. Impulse = F.T= ma . T= m . / T2 . T21 1 1m. . TTMLT kg m / s Ns l 14. 9011041155 / 90110311551412. Momentum = mv= m . / T= [ M1 L1T-1 ]= kg m / s13.31 3 0 3massDensityVolumemML T kg/m lM = [ M1L0T0] = [ M0L1T0]T = [ M0L0T1] 15. 9011041155 / 901103115515Uses of dimensional analysis1. To check correctness of equation.principle of homogeneity:- It states that dimensionstowards both sides of equation for each term aresame. Then the given equation is dimensionallycorrect.For e.g.1. 2 1s ut at2 s is displacementu = initial velocityt = timea = accelerationL.H.S = S = [ M0L0T1] .. (1)R.H.S 16. 9011041155 / 901103115516 ut = [ M0L1T-1] [ M0L0T1]= [ M0L1+0T-1+1]= [ M0L1T0] (2)2 1at2= [ M0L1T-2] [ M0L0T1]2= [ M0L1T-2] [ M0L0T2]= [ M0L1T0] .. (3)From (1), (2) & (3) we can say that the givenequation is dimensionally correct.2. v2 = u2 + 2as3. v = u + at4. w = w0 + mc2w = workw0 = workm = massc = speed of light 17. 9011041155 / 9011031155172. To find out conversion factor in between differentunits of same quantity .e.g.1 Let MKS unit of force if Newton (N)CGS unit of force is DyneLet 1 N = x dyneSubstituting dimensions of force in aboveequation,1 1 2 1 1 21 1 11 1 21 1 11 1 22M L T x MLTML TxMLTkg m s 2 g cm s 3 23 25510 10 cmgg cm10 10x 101N 10 dyne 1 J = x erg 18. 9011041155 / 901103115518e.g.2 v = u + at v = final velocity u = initial velocity a = acceleration t = time L.H.S = v v = [ M0L1T-1] (1) R.H.S = u u = [ M0L1T-1] (2) R.H.S at = [ M0L1T-2] [ M0L0T1] = [ M0L1T-1] (3) From (1), (2), (3) we can say that the given equation is dimensionally correct. 19. 9011041155 / 901103115519e.g. 3 v2 = u2 + 2as v = final velocity u = initial velocity a = acceleration s = displacement L.H.S = v2 v2 = [ M0L1T-1]2 = [ M0L1T-1] .. (1) R.H.S = u2 u2 = [ M0L1T-1] 2 = [ M0L2T-2] .. (2) as = [ M0L1T-2] [ M0L1T0] = [ M0L1+1 T-2+0] = [ M0L2T-2] .. (3) 20. 9011041155 / 901103115520From (1), (2), & (3) we can say that the given equation is dimensionally correct. e.g.4 w = w0 + mc2 w = work w0 = work m = mass c = speed of light L.H.S = w w = [ M1L2T-2] (1) R.H.S = w0 + mc2 w0 = [ M1L2T-2] (2) mc2 = [ M1L0T0] [ M0L1T-1]2 = [M1L0T0] [M0L2T-2] = [M1L0+2 T0-2] = [M1L2T-2]From (1), (2), & (3) we can say that the given equation is dimensionally correct. 21. 9011041155 / 9011031155211 J = x ergSubstituting dimensions of energy in aboveequation1 2 2 1 2 21 1 11 2 21 1 11 2 22 2M L T x ML TM L TxML Tkg m secx 2 2 g cm sec 23 102 cm 10gg cm x = 103 104 x = 107 1 J = 107 erg 22. 9011041155 / 901103115522 Ask Your Doubts For inquiry and registration, call 9011041155 / 9011031155.

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