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I Ir el, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , W_Basic Science-(Physics) (MSBTE - | Scheme) 1-3 Units and Measurements, — aa — ———_—, 1.1.2 Derived Physical Quantities Sr. Derived =| Unit Symbol |, gto The unit of d a No. physical, . eu erived physical Quantity is derived unit. quantity | j, Sr. Derived Unit Pa + ~, No. physical ymbol 24, | Angular | reat per square | rad/s, quantity acceleration secon | :, of 1 Ares 25. | Viscosity Newton second per | Ns/m |, 4 ; Square meter m square metre | |, " 2s Ve i |, re ‘olume Cubic meter m 26. | Electric field Volt per metre [vim |, 3. i i 7, Velocity Meter / second m/s 27. | Magnetic flux | tesla | Wb/m |, 4. | Acceleration Meter/ square m/s? density | |, zy second 28. | Magnetic field ] Ampere permetre | Alm |, 5. | Force Newton N strength I |, 6. | Pressure Newton/square Nim? 29. | Frequency Hertz [He |, any meter Prefixes of multiples and submultiples of units, j, led 7._| Work /Energy | Joule J Symbol Multiplier Prefix |, 8. Power Watt Ww T 10” tera |, t ;, 9. Electric Farad F 6 10° giga |, capacitance < 1, 10. | ind M 10 mega, . | Inductance Hen: H, as K 10° kile |, 11. | Momentum Kilogram + kg 2, B | h 10 hecto |, meter / second m/s 5 |, . 5 da 10 deca |, _| 12. | Surface tension | Newton / meter N/m oe a, 3 d 10 deci, _| 13. | Density Kilogram / cubic | kg/m T - 1, meter ¢ 10 centi |, i 3 P, | 14. | Electric charge | Coulomb c m 10 milli |, = ., > 15. | Electric Ohm Q u 10 micro, - 3, resistance nf 10 nano, | 16. | Electric Volt v p 10” pico, potential ; ; f 10° femto |, | 17. | Pressure Newton/square N/m a 10" auto |, J metre, 18. | Magnetic flux | weber Wb 1.1.3 Difference between Fundamental and, i Derived Quantity, 19. | Luminous flux lumen m, 7, 20. | illuminance candela/square cd/m Sr. Fundamental Derived quantity, ] metre No. | quantity, 21. | Specific heat Joule per Kilogram | J/kg °K a The physical quantities | The physical quantities, degree kelvin which do not depend on | which depend on one or, 22, | Thermal Watt per meter | W/m°K any other quantities for | more fundamental, ductivity degree kelvin. their measurement are | quantities for their, con - F ale called fundamental | measurement are called, Angular velocity | radian per secon: quantities. derived quantities., Wisi, , Scanned with CamScanner

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Accuracy in measurement can be predicted from:, (i) Process of measurement, , (ii) Use of measuring Instruments, , - Measurement is carried out by comparing the given, , physical quantity with standard., , - Any measurement consists of two parts e.g. mass of an, , object is 5 kg. Here, number 5 indicates the magnitude, and kg represents the standard. It is clearly, , understood that the mass of an object is 5 times the, standard., , \f all the quantities measured are clearly defined, there, is no chance of confusion between two persons., , e.g. If a person goes to a goods’ shop and asks for only, ‘2’ milk bags, shopkeeper will be confused whether to, give 2, ¥2 litre milk bags or 2, one litre milk bags. So, the measurement is not clearly defined in this case., , Measurement plays key role in development of, engineering and science., , Necessity of measurement in science, , 1. To identify various laws, , Relation between two or more quantities can be, , determined by measuring changes under variable, conditions., , e.g. Consider a gas of mass ‘m’ with constant, pressure (P). To determine the relation between, volume (V) and temperature (T), one has to check, the variations in V and T by accurate, measurement. At constant pressure it is observed, that volume (V) of a gas increases with increase in, absolute temperate (T). This is called Charles’ law., , 2. To verify various laws, , - If some statements or laws are to be verified,, then concerned physical quantities should be, measured accurately., , e.g. To verify series law of condensers, one should, calculate effective capacitance by formula and, compare it with experimental results., , Basic Science-(Physics) (MSBTE - | Scheme) 1-2, , Necessity of measurement in engineering, 1. Accurate prediction of physical quantities, , e.g. Measurement of length, mass, time, radius, has to, be clearly measured for developing engineering, products., 2. Quality assurance of products, , Quality depends on factors such as strength of, material, correctness, finishing, precision, flexibility,, etc. Before launching the product, all such factors are, measured by MQC department of a company., , 14.1. Fundamental and Derived Quantities, , 1.1.1. Fundamental Physical Quantities, , — The physical quantities which do not depend on any, other quantities for their measurement are called, fundamental quantities., , - The unit of fundamental quantity is fundamental unit., , There are 7 fundamental quantities as follows:, , , , , , , , , , , , , , , , , , , , , , , , Sr, Fundamental quantity Unit Symbol, , No,, , 1. | Length Meter m, , 2. | Mass Kilogram | kg, , 3. | Time Second | s :, , 4. | Electric current Ampere | A, , 5. | Thermodynamic Kelvin K, temperature, , 6. Amount of substance Mole mol _ |, , 7. | Luminous intensity Candela | cd |, , , , - Supplementary units:, , , , , , Sr, | Supplementary physical | Unit, , Symbol, No. | quantity, , , , , , 1. | Plane angle Radian rad, , , , , , 2. | Solid angle, , , , , , , , Steradian | sr, , , , , , , , , , , , hee Tack tnasnlelt, , Scanned with CamScanner

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Basic Science-(Physics) (MSBTE - | Scheme) 1, Sr. Fundamental Derived quantity, No. quantity, 2 The unit of fundamental | The unit of derived, quantity is called | quantity is called, fundamental unit. derived unit., , eH e.g. Length, mass, time, e.g. Force, area, density,, temperature, luminous velocity, pressure,, Intensity, electric | viscosity momentum., current, amount of, substance,, , , , , , , , 7 ay, , Units and Mensuremony, , 1.3 Dimensions and Dimensional Formula, Sa ee, 1.3.1 Dimensions, , Dimensions were first introduced by the French, Mathematician, Joseph Fourier., , , , , Definition : The dimensions of a physical quantity are the, powers to which the fundamental units of mass, length,, time, etc. must be raised to represent the given physica}, quantity., , , , , , 1.2 System of Units, 1.2.1 Unit of Physical Quantity, , , , Definition of unit : The standard used for measurement, of a physical quantity is called unit., , , , , , , , e.g. Length of wire is 1.5 m,, Here ‘m’ is a standard or unit of measurement of, length., , 1.2.2 Different Types of Systems of Units, , The base units for length, mass and time in these, systems are as follows:, , — In CGS system the base units are centimetre, gram and, second respectively., , — In FPS system (British system) the base units are Foot,, Pound and Second respectively., , - In MKS system the base units are Meter, Kilogram and, Second respectively., , — The system of units which is presently followed all, over the world uniformly is System International unit, or SI unit., , $1 standard includes symbols, units and abbreviations, developed by General Conference on Weights and, Measures in 1971 for international usage in scientific,, technical, industrial and commercial work., , — — Slunit used decimal system, so the conversions within, the system are easy and convenient., , , , , , , , , , , , , , , , , , , , , , , , , , , , , , 1.3.2 Dimensional Formula, , - The dimensional formula of a physical quantity is an, expression that describes the contribution of a, fundamental quantity into the unit., , - Fundamental quantities are represented by capital, letter. E.g. length (L), mass (M), time (T), electric, current (I), temperature (K) and luminous intensity (C)., , - Dimensional formula is obtained by using powers of, these capital letters within a square bracket., , 1.3.3. Applications of Dimensional Formula, 1. Checking the correctness of given equation, , 2. Conversion from one system to other, , 3. Derive relationships between physical quantities, , 4, Scaling and studying of models, , Principle of homogeneity, , — It states that an equation is dimensionally correct if, the dimensions of various terms on either side of, equation are the same., , - The principle is based on the fact that any two, quantities of same dimension only can be added up,, and resulting quantity also possesses the same, dimension., , e.g. Equation x4 y = 2 is valid only if dimensions of, , ro, Physical cGS MKS FPS SI yiyand@iaregame:, quantity, Length cm m ft m 1.3.4 Dimensional Constants, Velocity cm/s m/s fis mis Constants which possess dimensions are called, Force dyne | Newton Pound Newton dimensional constants., cya (N) force/ bf iN) e.g. Planck's constant., Heat cal kcal Btu Joule, energy = =a, , , , , , Scanned with CamScanner

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Basic Science-(Physics) (MSBTE - I Scheme), 1.4.2.5 Accidental Error, , These errors give very high or very low results., , Measurements involving these errors are not added in, calculations., , 1.4.2.6 Systematic Error, , These errors are normally in one direction, either, Positive or negative,, , These errors are caused due to defective setting or, adjustments of instrument by the user or due to some, , physical limitation of user such as poor eyesight, sense, of hearing, etc., , These errors can be minimized by finding cause of, , error and adopting the rules of Operation of that, instrument., , 1.4.3. Minimizing Errors, , Following rules can be adopted to minimize, errors, 1. Taking large magnitude of measurement of a quantity, 2. Using instrument with smallest possible least count, 3., , Taking large number of readings and calculating mean, value, , 1.4.4 Estimation of Errors, , After minimizing these errors, they can be estimated, to achieve better accuracy and precision in the, measurement of a physical quantity,, , Calibration of instrument is possible due to proper, estimation of error in the measurement., , 1.4.4.1 Calculating Error in the Measurement, , Let Ry, R,, Ry, . R, be the measured values of a, physical quantity in several measurements, then their, mean is considered as true value of that physical, quantity., , , , R, +R, +R,+, , True value (Ro) Rincan = n, , The magnitude of difference between the true value of, the physical quantity and the individual measurement, value is called absolute error in the measurement., , 1-6, , , , Units and Mea:, , Suremon|s, Therefore, absolute errors in measured values are, AR, = Ry-R,, AR, = Ry-R,, AR, = Ry-R;, AR, = RoR,, , The arithmetic mean of all the absolute errors is, known as mean absolute error., , ‘mean =, , AR, , The ratio of mean absolute error to mean value is, called relative error., , Mean absolute error, , Relative error, , Mean value, AR pean _ AR can, © Reean Ro, , Percentage error is the expression of the relative error, in percentage., , ‘mean, , , , , , Percentage error = Rercan x 100= R, x 100, 1.4.4.2. Combination of Errors, Case (i) If a quantity zis expressed as,, Z=xX+y or z=x-y, , then maximum value of error Az = Ax + Ay, , Hence when two quantities are added or subtracted,, , the absolute error in the final result is the sum of, absolute errors in the individual quantities., , Case (il) If quantity z is expressed as,, , z= xxy or 22%, ¥, Then maximum fractional error in z is given by,, az _ Ax Ay, zZ x" y, , Hence when two quantities are multiplied or divided,, , the relative error in the result is sum of relative errors, in the multipliers,, , Case (iii) ifz=x" y P etc, then maximum fractional error, is given by, , Az AY, , 7 = mtn 7 + ae, , , , , , Scanned with CamScanner

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WF Basic Science-(Physics) (MSBTE - 1 Schema), , 1.4.5 Dimensional Formulae of Some Physical Quantities, , Units and Measurements, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , Physical quantity Formula (By definition) Dimensional formula St unit, Area Length ngth x breadth L m, Volume Length x breadth x height vb m, Density mass 3 3, — M, volume ‘ Kalin, Velocity distance 1, ee UT, time ms, Acceleration velocity ix m/s?, time, Momentum mass x velocity mut * kg- m/s, Force mass x acceleration Mit? N, Energy, Work force x displacement MutT? J, OR (kg - m/s’), Power work mutT? WorJ/s, time, Frequency ES re Hz or /s, time, Pressure force mut? N/m’ or kg/ms’, area, Torque, Couple t=rFsin® mut? NmorJ, Moment of inertia l=mr mu kg: m, Heat energy QorH Mur? J, Temperature K K, Electric charge Qa QorT c, Entropy Energy MUT?K* J/K, time, Specific heat es —a_ unk I/kg+K, capacity meat, -2, Specific latent heat =a uy Ike, m, Thermal ae kA (0, - ®,) w/m+K, conductivity qd, -3,-2 2, Capacitance Q wi" a F, v, -1, Electric current 1 -2 torr A, By-ta=t I-32, Electric potential ya MLT Q> or MLT | Vv, 4ne,¢, , , , , , , , , , , , Scanned with CamScanner