Physics Unit & Dimension - JEE Main, JEE …

1 Corporate Office: CP Tower, Road , IPIA, Kota (Raj.), Ph: 0744-2434159 unit & DIMENSION1 unit & DIMENSIONC orporate Office: CP Tower, Road , IPIA, Kota (Raj.), Ph: 0744-2434159 unit & DIMENSION2 PrefaceIIT - JEE Syllabus : unit & DimensionIIT - JEE Syllabus : unit & DimensionIIT - JEE Syllabus : unit & DimensionIIT - JEE Syllabus : unit & DimensionIIT - JEE Syllabus : unit & DimensionUnit & dimensions , Dimensional analysis, Least count, Significant figure, Methods of measurementand Error analysis for physical concepts of the Physics start from this chapter. Basically the terms &concepts which are illustrated in this topic will be used in so many ways because all Physicalquantities have units.

2 It is must to measure all Physical quantities so that we can use them. In thischapter we will have an over view of different units of different Physical quantities. We will learnthe Dimension and dependence of the unit of any Physical quantity on fundamental quantities orunit. Entire topic is illustrated very systematically with respective examples so that the studentscan understand the fundamentals very easily & quickly. Students are advised to read every point ofsupplementary very carefully which is given at the end of the topic. Generally, students are notable to find out the Dimension of unseen or new quantity as their basic concepts are not clear &then they read the dimensions like a parrot.

3 It should be avoided & they should develope themselves,so that they can find out the dimensions of any given number of Questions in Units & Dimension are :In chapter 27 unit & DIMENSIONC orporate Office: CP Tower, Road , IPIA, Kota (Raj.), Ph: 0744-2434159 unit & DIMENSION3 Physics : Physics is the study of the laws of nature fromthe observed events. 1. PHYSICAL QUANTITIES The quantities by means of which we describethe laws of Physics are called physical are two type of physical Fundamental Derived Fundamental quantities:Physical quantities which are independent of eachother and cannot be further resolved into anyother physical quantity are known as fundamentalquantities.

4 There are seven (a) LengthMetrem(b) MassKilogramkg(c) TimeSeconds(d) Electric currentAmpereA(e) ThermodynamicKelvinKtemperature(f) LuminousCandelaCdintensity(g) Amount Derived Quantities :Physical quantities which depend uponfundamental quantities or which can be derivedfrom fundamental quantities are known as derivedquantities. 2. UNITS Definition : Things in which quantity is measuredare known as of physical quantity= (Magnitude) ( unit ) physical quantity is measured and the resultis expressed as nu where u is the unit usedand n is the numerical value. If the result isexpressed in various units then :(A) n size of u (B) n u2(C) n u(D) n u1 Answer : (D)There are three types of Fundamental or base Derived Supplementary Fundamental or base units:Units of fundamental quantities are calledfundamental Characteristics of fundamental units:(i) they are well defined and are of a suitable size(ii) they are easily reproducible at all places(iii) they do not vary with temperature, timepressure etc.

5 Invariable.(iv) there are seven fundamental Definitions of fundamental :The distance travelled by light in Vacuum in458,792,2991 second is called :The mass of a cylinder made of platinum iridiumalloy kept at international bureau of weights andmeasures is defined as :Cesium -133 atom emits electromagnetic radiationof several wavelengths. A particular radiation isselected which corresponds to the transistionbetween the two hyperfine levels of the groundstate of Cs - 133. Each radiation has a timeperiod of repetition of certain characteristics. Thetime duration in 9, 192, 631, 770 time periods ofthe selected transistion is defined as :Suppose two long straight wires with negligiblecross-section are placed parallel to each other invacuum at a seperation of 1m and electriccurrents are established in the two in samedirection.

6 The wires attract each other. If equalcurrents are maintained in the two wires so thatthe force between them is 2 10 7 newton permeter of the wire, then the current in any of thewires is called 1A. Here, newton is the SI unit :The fraction 1273 the thermodynamictemperature of triple point of water is called Office: CP Tower, Road , IPIA, Kota (Raj.), Ph: 0744-2434159 unit & :The amount of a substance that contains as manyelementary entities (Molecules or atoms if thesubstance is monoatomic) as there are numberof atoms in .012 kg of carbon - 12 is called amole. This number (number of atoms in kgof carbon-12) is called Avogadro constant and itsbest value available is x 1023.

7 :The unit of luminous intensity is 1cd whichis the luminous intensity of a blackbody ofsurface area 1600 000,m2 placed at thetemperature of freezing platinum and at a pressureof 101,325 N/m2, in the direction perpendicular toits on Definition of fundamental man seeing a lighting starts countingseconds until he hears thunder. He thenclaims to have found an approximate butsimple rule that if the count of second isdivided by an integer, the result directly givesin km, the distance of the lighting is the integer if the velocity of sound is330 n is the integer then according to theproblem tinsn = dist in km.

8 Tinsn = (v) tn = 1v = 1330 103x = defining the standard of length we have tospecify the temperature at which themeasurement should be made. Are wejustified in calling length a fundamentalquantity if another physical. quantity,temperature, has to be specified in choosinga , length is a fundamental quantity. Onemetre is the distance that contains1650 wavelength of orange-red light ofKr - 86. Hence, the standard metre isindependent of temperature. But the lengthof object varies with temperature and is givenby the relation .Lt = L0 (1 + t) We usually specify the temperature atwhich measurement is of the following sets cannot enter intothe list of fundamental quantities in anysystem of units(A) length ; mass ; velocity(B) length ; time ; velocity(C) mass ; time; velocity(D) length ; time, massSol.

9 [B] Since velocity = lengthtime in this set aquantity is dependent on the other twoquantities Where as fundamental quantitiesare Derived units :Units of derived quantities are called derived units. Physical quantityunits llustration Volume = (length)3 m3 Speed = length/time Supplementary units :The units defined for the supplementary quantitiesnamely plane angle and solid angle are calledthe supplementary units. The unit for plane angleis rad and the unit for the solid angle is :The supplemental quantities have only units butno dimensions (will be discussed later) 3. PRINCIPAL SYSTEM OF UNITS system [centimetre (cm) ; gram (g) and second (s)] system [foot ; pound ; second] system [meter ; kilogram ; second] (system of international)In 1971 the international Bureau of weight andmeasures held its meeting and decided a systemof units.

10 Which is known as the internationalsystem of Office: CP Tower, Road , IPIA, Kota (Raj.), Ph: 0744-2434159 unit & DIMENSION5 Examplesbased on acceleration due to gravity is is its value in ft/s2 ? 1 m = ft, m/s2 = ft/s2 = cheap wrist watch loses time at the rate second a day. How much time will thewatch be off at the end of a month ? delay = s/day= 30 s/ (30 day)= 255 s/month = min/month. 5. DIMENSIONAL FORMULA It is an expression which shows how and which of the fundamental units are required to represent the unitof physical quantities with units.