Title 1. Physical World and Measurement.pdf ✅

Physical World and Measurement 1 1 Physical World and Measurement QUICK LOOK Neither the names nor the symbols used for the physical quantities are international standards. Some quantities are known as several different names such as the magnetic B-field which known as the magnetic flux density, the magnetic induction or simply as the magnetic field depending on the context. Similarly, surface tension can be denoted by σ γ, or T. The table usually lists only one name and symbol. The final column lists some special properties some of the quantities have such as their scaling behavior (i.e. whether the quantity is intensive or extensive), their transformation properties (i.e. whether the quantity is a scalar, vector or tensor) or whether the quantity is conserved. Table 1.1: Base Quantities Base quantity Symbol Description SI unit Symbol for dimension Comments / Definition length l The one-dimensional extent of an object. metre (m) L 1 metre = the length of the path traveled by light in vacuum during a time interval of 1 / 299 792 458 of a second. (17th CGPM, 1983, Resolution 1) Mass m The amount of matter in an object. kilogram (kg) M Extensive/1 kilogram = the mass of the international prototype of the kilogram. (3rd CGPM, 1901) Time t The duration of an event. second (s) T 1 second = the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom. (13th CGPM, 1967, Resolution 1) Electric current I Rate of flow of electrical charge. ampere (A) I 1 ampere = that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vaccum, would produce between these conductors a force equal to 2 · 10–7 newton per metre of length. (9th CGPM, 1948) Temperature T Average energy per degree of freedom of a system. kelvin (K) θ Intensive/1 kelvin = the fraction 1 /273.16 of the thermodynamic temperature of the triple point of water. (13th CGPM, 1967) Amount of substance n Number of particles compared to the number of atoms in 0.012 kg of 1 2 C . mole (mol) N Extensive/1 mole = the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon – 12. (14th CGPM, 1971) Luminous intensity L Amount of energy emitted by a light source in a particular direction. candela (cd) J 1 candela = the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 · 1012 hertz and that has a radiant intensity in that direction of 1 / 683 watt per steradian. (16th CGPM, 1948) To convert a physical quantity from one system to the other 1 1 1 2 1 2 2 2 a b c M L T n n M L T       =             Table: 1.2 Physical Quantities Derived quantity Symbol Description SI units Dimension Comments Plane angle θ Measure of a change in direction or orientation. radian (rad) 1 Solid angle Ω Measure of the size of an object as projected on a sphere. steradian (sr) 1 Absorbed dose rate Absorbed dose received per unit of time. Gy s –1 L 2 T−3 Angular momentum L Measure of the extent and direction and object rotates about a reference point. kg m 2 s –1 M L2 T−1 conserved quantity, pseudovector Area A The two-dimensional extent of an object. m 2 L 2 Area density ρA The amount of mass per unit area of a two- dimensional object. kg m –2 M L−2
2 Quick Revision NCERT-PHYSICS Capacitance C Measure for the amount of stored charge for a given potential. Fara (F = A 2 ) s 4 kg−1 m −2) I 2 T4 M−1 L −2 Catalytic activity Change in reaction rate due to presence of a catalyst. katal (kat = mol s−1) N T−1 Catalytic activity concentration Change in reaction rate due to presence of a catalyst per unit volume of the system. kat m−3 N L−3 T−1 Chemical potential Μ The amount of energy needed to add a particle to a system. J mol−1 M L2 T−2 N −1 intensive Molar concentration C Amount of substance per unit volume. mol m −3 N L−3 intensive Current density J Amount of electric current flowing through a surface. A m−2 I L−2 vector Dose equivalent H Measure for the received amount of radiation adjusted for the effect of different types of radiant on biological tissue. sievert (Sv = m2 s−2) L 2 T−2 Dynamic Viscosity Η Measure for the resistance of an incompressible fluid to stress. Pa s M L−1 T−1 Electric Charge Q Amount of electric charge. coulomb (C = A s) I T extensive, conserved quantity Electric charge density ρQ Amount of electric charge per unit volume. C m−3 I T L−3 intensive Electric displacement D Strength of the electric displacement. C m−2 I T L−2 vector field Electric field strength E Strength of the electric field. V m−1 M L T−3 I−1 vector field Electrical conductance G Meausure for how easily current flows through a material. siemens (S = A2 s3 kg−1 m −2) L −2 M −1 T 3 I 2 scalar Electric potential V The amount of work required to bring a unit charge into an electric field from infinity. volt (V = kg m2 A−1 s−3) L 2 M T−3 I−1 scalar Electrical resistance R The degree to which an object opposes the passage of an electric current. ohm (Ω = kg m2 A−2 s−3) L 2 M T−3 I−2 scalar Energy density ρE Amount of energy per unit volume. J m−3 M L−1 T−2 intensive Entropy S Measure for the amount of available states for a system. J K−1 M L2 T −2 Θ −1 extensive, scalar Impulse p The cause of a change in momentum, acting on an object. kg m s−1 M L T−1 vector Frequency F The number of times something happens in a period of time. hertz (Hz = s−1) T −1 Half-life t1/2 The time needed for a quantity to decay to half its original value. S T Heat Q Amount of energy transferred between systems due to temperature difference. J M L2 T−2 Heat capacity Cp Amount of energy needed to raise the temperature of a system by one degree. J K−1 M L2 T −2 Θ −1 extensive Heat flux density φQ Amount of heat flowing through a surface per unit area. W m−2 M T−3 Illuminance Ev Total luminous flux incident to a surface per unit area. lux (lx = cd sr m−2) J L−2 Impedance Z Measure for the resistance of an electrical circuit against an alternating current. ohm (Ω = kg m2 A−2 s−3) L 2 M T−3 I−2 complex scalar Index of refraction n The factor by which the speed of light is reduce in a medium. 1 intensive Inductance L Measure for the amount of magnetic flux generated for a certain current run through a circuit. henry (H = kg m2 A−2 s −2) M L2 T−2 I−2 Irradiance E Power of electromagnetic radiation flowing through a surface per unit area. W m−2 M T−2 Linear density ρl Amount of mass per unit length of a one-dimensional object. M L−1 Luminous flux (or luminous power) F Perceived power of a light source. lumen (lm = cd sr) J Magnetic field strength H Strength of a magnetic field in a material. A m−1 I L−1 vector field Magnetic flux Φ Measure of quantity of magnetism, taking account of weber (Wb = kg m2 A−1 M L2 T−2 I−1 scalar

4 Quick Revision NCERT-PHYSICS Limitations of Dimensional Analysis: Although dimensional analysis is very useful it cannot lead us too far as, If dimensions are given, physical quantity may not be unique as many physical quantities have same dimensions. For example if the dimensional formula of a physical quantity is 2 2 [ ] ML T − it may be work or energy or torque. Numerical constant having no dimensions [K] such as (1/2), 1 or 2π etc. cannot be deduced by the methods of dimensions. The method of dimensions cannot be used to derive relations other than product of power functions. For example, 2 s u t a t = + (1/ 2) or y a t = sinω cannot be derived by using this theory (try if you can). However, the dimensional correctness of these can be checked. The method of dimensions cannot be applied to derive formula if in mechanics a physical quantity depends on more than 3 physical quantities as then there will be less number (= 3) of equations than the unknowns (> 3). However still we can check correctness of the given equation dimensionally. For exampleT mgl = 2 1 π can not be derived by theory of dimensions but its dimensional correctness can be checked. Even if a physical quantity depends on 3 physical quantities, out of which two have same dimensions, the formula cannot be derived by theory of dimensions, e.g., formula for the frequency of a tuning fork 2 f d L v = ( / ) cannot be derived by theory of dimensions but can be checked. Accuracy: Accuracy of a result or experimental procedure can refer to the percentage difference between the experimental result and the accepted value. The stated uncertainty in an experimental result should always be greater than this percentage accuracy. Accuracy is also associated with the inherent uncertainty in a measurement. We can express the accuracy of a measurement explicitly by stating the estimated uncertainty or implicitly by the number of significant figures given. For example, we can measure a small distance with poor accuracy using a metre rule, or with much greater accuracy using a micrometer. Another term you will hear in relation to experiments and experimental results is the term precision. Precision is the degree of exactness with which a quantity is measured. Nature and Use of Errors: Errors occur in all physical measurements. When a measurement is used in a calculation, the error in the measurement is therefore carried through into the result. The two different types of error that can occur in a measured value are: Systematic error: This occurs to the same extent in each one of a series of measurements eg zero error, where for instance the needle of a voltmeter is not correctly adjusted to read zero when no voltage is present. Random error: This occurs in any measurement as a result of variations in the measurement technique (eg parallax error, limit of reading, etc). Experimental Errors: The variations in different readings of a measurement are usually referred to as “experimental errors”. They are not to be confused with “mistakes”. Such variations are normal. Precise Measurement: Least count = one division value of main scale / Total number of divisions on vernier or circular scale Figure 1.1 Least count of vernier calipers, s LC n = Least count of screw guaze p n = Error in a measurement = Least count. Percentage error in a formula a b c p q y r = is 100% p q r a b c p q r   ∆ ∆ ∆   + + ×   The last figure in a measurement is doubtful, the error in last figure is ± 1. (Keeping position with respect to decimal place fixed.) Figure 1.2 0 20 15 10 5 Anvil Spindle Sleeve Thimble Ratchet Frame Main scale Rotating scale d Knife-edge measuring faces for inside measurement Slide Guide bar Vermier Graduated scale Fixed jaw bade Measuring faces for outside measurement Movable jaw blade Measuring faces for depth measurement Depth measuring