UNITS AND MEASUREMENTS

Transcription

1 UNITS AND MEASUEMENTS. Physics is a science of measurments. PHYSICAL QUANTITY: Any quantity which canbe measured directly (or) indirectly (or) in terms of which any laws of physics can be expressd is called physical quantity. 3. There are two types of physical quantities ) Fundamental quantity ) Derived quantity ) Fundamental Quantity : Physical Quantities which cannot be expressed in terms of any other physical quantites are called fundamental physical quantities. E.g. length, mass, time, temperature etc.. ) Derived Quantity :Physical Quantities which are derived from fundamental quantities are called derived quantities. E.g. Area, density, force etc... UNIT OF MEASUEMENT:. A fixed measurement chosen as a standard of measurement to measure a physical quantity is called a Unit.. To measure a physical quantity means to determine the number of times its standard unit contained in that physical quantity. 3. A standard Unit is necessary for the sake of. accuracy,. convenience, 3. unformity and 4. equal justice to all. 4. The standard unit chosen should have the following characteristics.. Consistency (or) invariability. Availability (or) reproducibility 3. Imperishability (Permanency) 4. Convenience and acceptability 5. The measure of a Physical Quantity is given by a numerical value and a unit. x nu where x is the measure of a physical quantity, n is numerical value and u is the unit. 6. The numerical value obtained on measuring a physical quantity is inversely proportional to the magnitude of the unit chosen. n U nu nu Where n and n are the numerical values and U and U are the units of same physical quantity in different systems. Fundemental unit :The unit used to measrue the fundamental quantity is called fundamental unit. e.g., Metre for length, kilogram for mass etc.. Derived unit : The unit used to measure the derived quantity is called derived unit. e.g., m for area, gm cm -3 for density etc... FUNDAMENTAL QUANTITIES AND THEI S.I. UNITS:. There are seven basic quantities and two supplementary quantities in S. I. system. The names and units with symbols are given below: S.No. Physical Quantity S.I.Unit Symbol. Length metre m. Mass kilogram kg 3. Time second s 4. Themro dynamic

2 temperature Kelvin K (or) 5. Luminous intensity candela Cd 6. Electric current ampere A 7. Amount of substance (or) quantity of matter mole mol Suplementary quantities. Plane angle radian rad. Solid angle steradian sr. DEFINITIONS FO S.I. UNITS:. meter: meter is in 99, 79, 458th part of the distance travelled by light in vaccum in second.. Kilogram:Kilogram is the mass of a platinum - irridium alloy cylinder proto type kept at Serves, near Paris. 3. second: One second is the time taken by 9, 9, 63, 770 cycles of the radiation from the hyperfine transition in ceasium - 33 atom, when unperturbed by external fields. 4. Kelvin: This is /73. 6 of the temperature at the triple point of water measured on thermodynamic scale. 5. Candela: Candela is the luminous intensity in a direction normal to the surface of m of a black body at the temperature of freezing platinum at a pressure of 0, 35 newton per square metre. 6. ampere: ampere is the current which when flowing in each of two parallel conductors of infinite length and negligible cross-section and placed one metre apart in vaccum causes each conductor to experience a force exactly x0-7 newton per metre length. 7. mole: mole is the amount of substance of a system that contains as many elementary entities as there are atoms in 0.0 kg of carbon radian: radian is the angle subtended at the centre of a circle by an arc whose length is equal to the radius. radian = : radian = 360 = 570 7' 44" 9. Steradian: The solid angle subtended at the centre of the sphere of radius metre by its surface of area square metre. Solid angle= normal area/r. Total solid angle that can be formed at any point in space or at the centre of a sphere is 4 steradian. 3. Other conventional units of fundamental quantities : Length : micron 6 0 m to express the size of bacteria, animal cells etc., Angstrom unit 0 0 m to express the wavelength of light X-ray unit 3 0 m for wavelength of x-rays Fermi 5 0 m to express the size of nucleus Light year m to express astronomical distances per sec 3.6 light years m to express astronomical distances Bohr radius m Mass : Quintal = 00 Kg Metric ton = 000 Kg

3 7 Atomic mass unit (a.m.u) =.670 Kg Chandra Shekar Limit =.4 times mass of the sun Time : One day = seconds Shake = 8 0 sec PEFIXES: (or) Abbreviations for multiples andsub-multiples of 0. MACO Prefixes MICO Prefixes Kilo K 0 3 milli m 0-3 Mega M 0 6 micro 0-6 Giga G 0 9 nano n 0-9 Tera T 0 pico p 0 - Peta P 0 5 femto f 0-5 Exa E 0 8 atto a 0-8 Zetta Z 0 zepto z 0 - Yotta Y 0 4 yocto y 0-4 Note: The following are not used in SI system. deca 0 deci 0 - hecta 0 centi 0 - ULES FO WITING UNITS:. Symbols for a unit named after a scientist should have a capital letter. eg:n for newton, W for watt, A for ampere.. Full names of the units,even when they are named after a scientist should not be written with a capital letter. Eg: newton, watt, ampere, metre. 3. Units should be written either in full or in agreed symbols only. 4. Units do not take plural form. Eg: 0kg but not 0 kgs, 0W but not 0 Ws A but not As 5. No full stop or punctuation mark should be used within or at the end of symbols for units. Eg: 0W but not 0W. DIMENSIONS OF PHYSICAL QUANTITY:.Dimensions: Dimensions of a physical quantity are the powers to which the fundamental units are to be raised to obtain one unit of that quantity.dimensional Formula : An expression showing the powers to which the fundamental units are to be raised to obtain one unit of the derived quantity is called Dimensional formula of that quantity. 3. Dimensional Constants: The physical quantities which have dimensions and have a fixed value are called dimensional constants. Eg: Gravitational Constant (G), Planck's Constant (h), Universal gas constant (), Velocity of light in vacuum (c) etc., 4. Dimensionless constants: Dimensionless quantities are those which do not have dimensions but have a fixed value. (a): Dimensionless quantities without units. Eg: Pure numbers,, e, Sin, Cos, tan...etc., (b) Dimensionless quantities with units. Eg: Angular displacement - radian, Joule's constant- joule/calorie, etc., 5. Dimensional variables: Dimensional variables are those physical quantities which have dimensions and do not have fixed value. Eg: velocity, acceleration, force, work, power... etc.

4 6. Dimensionaless variables: Dimensionless variables are those physical quantities which do not have dimensions and do not have fixed value., Eg: Specific gravity, refractive index, Coefficient of friction, Poisson's atio etc., PHYSICAL QUANTITES HAVING SAME DIMENTIONAL FOMULAS. Distance, Displacement, radius light year wavelength, radius of gyration (L). Speed, Velocity, Velocity of light LT 3. acceleration,acceleration due to gravity, intensity of gravitational feild, centripetal acceleration LT 4. Impulse, Change in momentum MLT 5. Force, Weight, Tension, Thrust MLT 6. Work, Energy, Moment of force or Torque, Moment of couple ML T 7. Force constant, Surface Tension, Spring constant, Energy per unit area MT 8. Angular momentum, Angular impulse, Plank's constant ML T 9. Angular velocity, Frequency, Velocity gradient, Decay constant, rate of disintigration (T ) 0. Stress, Pressure, Modulus of Elasticity, Energy density ML T. Latent heat, Gravitational potential L T. Specific heat, Specific gas constant L T 3. Thermal capacity, Entropy, Boltzman constant, Molar thermal capacity, ML T 4. Wave number, Power of a lens, ydberg constant L 5. Time, C, L, LC T 6. Power, ate of dissipation of energy, ( 3 ML T ) 7. Intensity of sound, Intensity of radiation ( 3 MT ) 8. Expansion coefficient, Temperature coefficient of resistance ( K ) 9. Electric potential, potential difference, electromotive force ( 3 ML T I ) 0. Intensity of magnetic field, Intensity of magnetization IL Principle of homogenity: It states only quantities of same diemensions can be added subtracted and equated. Hence in a Physical equation every term should have same dimensions. USES OF DIMENSIONAL EQUATIONS: I. Use: To check the correctness of the given equation. This use is based on the principle of homogenity. II. Use: To convert one system of units into another system. Eg: The numerical value of 0 joule in a new system of units in which the unit of mass is 0gm, unit of length 0cm. and unit of time 0sec. is ---- using since. a b c a b c since n n M L T [ ] [ ]

5 THE FOLLOWING IS THE LIST OF SOME PHYSICAL QUANTITIES WITH THEI FOMULAE AND DIMENSIONAL FOMULAE Sl.No. Physical Quantity Explanation or Formulae Dimensional C.G.S. Unit S.I.Unit Formulae. Distance : ( Length ) L Displacement ( S ) Wave Length ( ) adius of gyration () Circumference Perimeter Light year Par-sec S C P L.Y Par-sec. Mass Measure of inertia total time 3. Period of oscillation, T = N o. of oscillations Time, Time constant T = Capacity x esistance 4. Frequency eciprocal of time n T M L T 0 0 Cm m M L T 0 0 gm Kg 0 0 S S 0 0 S ( hz) hertz ( Hz) 5. Area A = l x b ( or) L 0 0 cm ( sq.cm) m ( sq.m) 6. Volume V = L.b. h. (or) L cm 3 m 3 (cubic ( Cubic cm ) metre) Mass M Density D Volume L 3 gm. cm -3 kg.m Linear density 9. Speed (scalar) M m L ( Massper unit length) 0 gm.cm - kg.m - Velocity ( Vector) V = L T 0 cm s - m.s - dv Change in Velocity 0. Acceleration a = dt time 0 cm s - m.s -. Linear Momentum P M V. Impulse J F. t 3. Force F = M.a 4. Work W = F x S Energy P.E= mgh KE = M LT gm.cms - kg.m.s - M LT dyne-s N-S M LT dyne. newton ( gm cm s - ) = (kg.m.s - ) MV erg=dyne-cm Joule Strain energy =Newton-m = Stress Strain volume ( gm.cm s - ) ( kg.m s - )

6 5. Power 6. Pressure Stress P Work time 3 Force Area erg s - J.S -. (or) Watt 7. Strain Modulus of Elasticity Stress y Strain dyne - cm - N.m -. (or) y, n, k Pascal e l No Units Strain energy density E = Work Volume erg.cm -3 J.m Angular displacement 0. Angular Velocity. Anuglar acceleration l r radian radian d 0 0 dt rad.s - rad.s - d d 0 0 dt dt rad s - rad.s -. Angular momentum L r p rmvsin gm.cm s - kg.m s - 3. Planck's constant h E erg-s J -S 4. Angular impulse Torque time erg-s J.s 5. Torque r F r M a Sin dyne-cm N-m 6. Acceleration due to gravity(g)= gravitational F g M 0 M LT cm.s - m.s - field strength = [dyne.gm - ] [N.kg - ] 7. Universal gravitational G F. d M. M 3 dyne.cm.gm - N.m kg - Constant or or [gm - cm 3 s - ] [kg -.m 3.s - ] 8. Moment of inertia 9. Velocity gradient I MK dv dx 0 gm.cm kg.m 0 0 S S 30. Surface Tension, F E S or L A 0 dyne.cm - N.m - Spring Constant ( Surface energy) = erg. cm - = J.m - Force Constant F K e

7 3. Coefficient of Viscosity F dv A. dx pressure x time POISE Pa-s dyne s cm Ns m 3. Gravitational Potential Work Mass 0 erg.gm - J.Kg Heat energy energy Calorie Joule 34. Temperature (or) Kelvin c Kelvin( K) dq 35. Thermal Capacity Mass Sp. ht d. Cal/ 0 c J. K Specific heat Capacity S (or) C 37. Latent heat (or) Calorific value L Q M Q M 0 0. Cal / gm / 0 c J kg - K - Cal.gm - J.kg Water Equivalent W MC grms 0 0 gm kg. 39. Coefficient of Thermal or or expansion 40. Universal gas constant ( for Mole) 4. Gas constant ( for gram) 4. Boltzman constant (for Molecule) 43. Mechanical equivalent of heat 44. Coefficient of Thermal Conductivity 45. Entropy l ; l. r k J PV nt A V ; A. V. Mol. wt 0 AvagadroNo. W H K Q. d A. t dq d 0 c - K - M L: T mol erg.mol -. 0 c - J.mol -.K - M L: T mol erg.gm -.c - J.kg - K - M L : T erg.gm -.c - J.K - erg/cal or J/cal molecule - 3 M LT Cal s - cm - 0 c - J.S - m - K -. erg 0 c - J.K - or w.m - K Stefan's Constant E 4 A. T k erg/scm / 0 c 4 J/sm /K 4 (or) W.m -.K -4

8 47. Thermal resistance d temp time dq Heat dt 3 K ---- KSJ - ( or) d K. A 48. Temperature gradient Change in t emp d L length dl 0 c. cm K.m Pressure gradient Change in pressure length dp dl dyne.cm - pascal.m Solar constant Energy E area time AT. 0 3 erg.s -.cm - J.S -.m - (W.m - ) 5. Enthalpy heat.( Q) Calorie Joule 5. Pole strength m I. L ( or) 0 0 M LT. A --- amp-metre Magnetic M omement Mag. Length 53. Magnetic Moment M l. m A.m Current area pole m 54. Magnetic intensity (or) H 4 d Magnetising field strength x length of the Magnet 0 0 (A.m) Oersted A.m Intensity of Magnetisation M Magnetic Moment I V Volume 0 M L T 0 A A.m Magnetic flux B A Maxwell Weber ( wb) =(magnetic induction x area) 57. Magnetic induction (or) Magnetic flux F B 0 A area il. A gauss tesla (or) field strength web. m Magnetic permeability of free space 59. Magnetic susceptibility N.A -.m - 4. Fd 0 m. m M LT. A e.m.u henry.m - K I H No. Units Electric current elementary quantity stat amp. ampere 6. Charge ( or) Electricity Q I T Current x time 0 0. A Stat coulomb Coulomb 6. Electric dipole moment P Q d Charg e dis tan ce 0 0. A Stat.coul-cm coulombmet 63. Electric field strength (or) Elec. Intensity F Force E Q Ch arg e M LT 3 A dyne/stat.coul. Nc -

9 64. Electrical flux ( E ) Electrical Intensity x area N.m C Electric potential (or) Potential difference 66. Electrical resistance 67. Electrical conductance 68. Specific resistance (or esistivity (or) s 69. Electrical conductivity V Work Ch arg e 3 Pot. diff Current 3 Stat Volt Volt.(V) Stat - Ohm Ohm-( ) C resis tan ce M L T 3 A mho (or) Siemen (S). A l 3 3 A Ohm-m e sistivity Current density ( Current per unit area J = Electrical Intensity x Conductivity Current of cross section) or area 7. Capacitance C= Q Ch arg e V Potential 4 de Voltage time 7. Self (or) Mutual Inductance L di Current dt 73. Electrical permitivity of free space q. q 4 fd Ohm - -m -( (or) Siemen/ metre 0 0 A.m - farad henry (or) Weber/amp. farad/m 74. Surface density of Charge Ch arg e area 0 C.m Luminous flux Light energy time 3 Lumen 76. Intensity of illumination (or) Iluminance 77. Focal Power 78. Wave number (Propagation constant) 79. ydberg constnat E Lu minious flux I t. A area P v focal length Luman.m Z e m 3 8 0ch M 0 L T 0 cm - m - cm - m - (or) Lux. Dioptre