{"id":34584,"date":"2022-11-23T17:17:38","date_gmt":"2022-11-23T11:47:38","guid":{"rendered":"https:\/\/tsboardsolutions.com\/?p=34584"},"modified":"2022-11-23T17:17:38","modified_gmt":"2022-11-23T11:47:38","slug":"ts-inter-1st-year-physics-notes-chapter-2","status":"publish","type":"post","link":"https:\/\/tsboardsolutions.com\/ts-inter-1st-year-physics-notes-chapter-2\/","title":{"rendered":"TS Inter 1st Year Physics Notes Chapter 2 Units and Measurements"},"content":{"rendered":"<p>Here students can locate <a href=\"https:\/\/tsboardsolutions.com\/ts-inter-1st-year-physics-notes\/\">TS Inter 1st Year Physics Notes<\/a> 2nd Lesson Units and Measurements to prepare for their exam.<\/p>\n<h2>TS Inter 1st Year Physics Notes 2nd Lesson Units and Measurements<\/h2>\n<p>\u2192 Fundamental Quantity : A fundamental quantity is one which is unique and freely existing. It does not depend on any other physical quantity. Ex: Length (L), Time (T), Mass (M) etc.<\/p>\n<p>\u2192 Fundamental quantities in SI System : In SI system length, mass, time, electric current, thermodynamic temperature, amount of substance and luminous intensity are taken as fundamental quantities.<\/p>\n<p>\u2192 Derived quantity: A derived quantity is pro-duced by the combination of fundamental quantities (i.e., by division or by multiplica-tion of fundamental quantities).<br \/>\nEx: Velocity = \\(\\frac{\\text { displacement }}{\\text { time }}=\\frac{\\mathrm{L}}{\\mathrm{T}}\\) or LT<sup>-1<\/sup><br \/>\nAcceleration = \\(\\frac{\\text { change in velocity }}{\\text { time }}\\)<br \/>\n= \\(\\frac{\\mathrm{LT}^{-1}}{\\mathrm{~T}}\\) = LT<sup>2<\/sup><\/p>\n<p>\u2192 Unit: The standard which is used to measure the physical quantity is called the Unit&#8217;.<\/p>\n<p>\u2192 Fundamental unit: The units of the funda-mental quantities are called the &#8220;fundamental units&#8221;.<br \/>\nEx : Length \u2192 Meter (m), Mass \u2192 Kilogram (kg), Time Second (sec) etc.<\/p>\n<p>\u2192 Basic units or fundamental units of SI system : The basic units in S.I. system are Length \u2192 metre (L), Mass \u2192 kilogram (kg), Time second (s); electric current \u2192 ampere (amp), Thermodynamic temperature \u2192 Kelvin (K); Amount of substance \u2192 mole (mol); Luminous intensity \u2192 candela (cd); Auxilliary units : Plane angle \u2192 Radian (rad); Solid angle \u2192 steradian (sr)<\/p>\n<p>\u2192 Derived units: The units of derived quantities are known as &#8220;derived units&#8221;.<br \/>\nEx: Area \u2192 square meter (m<sup>2<\/sup>),<br \/>\nVelocity \u2192 meter\/sec (m\/s) etc.<\/p>\n<p>\u2192 International system of units (S.I. units) :<br \/>\nS.I. system consists of seven fundamental quantities and two supplementary quantities. To measure these quantities S.I. system consists of seven fundamental or basic units and two auxiliary units.<\/p>\n<p>\u2192 Accuracy: Accuracy indicates the closeness of a measured value to the true value of the quantity. If we are very close to the true value then our accuracy is high.<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/tsboardsolutions.com\/wp-content\/uploads\/2022\/10\/TS-Board-Solutions.png\" alt=\"TS Inter 1st Year Physics Notes Chapter 2 Units and Measurements\" width=\"183\" height=\"15\" \/><\/p>\n<p>\u2192 Precision : Precision depends on the least measurable value of the instrument. If the least measurable value is too less, then precision of that instrument is high.<br \/>\nEx : Least measured value of vernier callipers is 0.1 mm<br \/>\nLeast count of screw gauge is 0.01 mm.<br \/>\nAmong these two, the precision of the screw gauge is high.<\/p>\n<p>\u2192 Error: The uncertainty of measurement of a physical quantity is called &#8220;error&#8221;.<br \/>\n\u2192 Systematic errors : Systematic errors always tend to be in one direction i.e., positive or negative. For systematic errors, we know the reasons for the error. They can be reduced by proper correction or by proper care. Ex:<\/p>\n<ul>\n<li>Zero error in screw gauge and<\/li>\n<li>A faulty calibrated thermometer<\/li>\n<\/ul>\n<p>Note :<br \/>\nSystematic errors are classified as<\/p>\n<ul>\n<li>Instrumental errors<\/li>\n<li>Imperfection of experimental technique<\/li>\n<li>Personal errors.<\/li>\n<\/ul>\n<p>1) Instrumental errors: These errors arise due to the imperfect design or faulty calibration of instruments.<br \/>\nEx : Zero error in screw gauge.<\/p>\n<p>2) Imperfection of experimental technique: These errors are due to the procedure followed during experiment or measurements. Ex : 1) Measurement of body temperature at armpit 2) Simple pendulum oscillations with high amplitude.<\/p>\n<p>3) Personal errors: These errors arise due to an individual\u2019s approach or due to lack of proper setting of apparatus.<br \/>\nEx : Parallax error is a personal error.<\/p>\n<p>\u2192 Methods To Reduce Systematic Errors :<br \/>\nSystematic errors can be minimized by improving experimental techniques, by selecting better instruments and by removing personal errors.<\/p>\n<p>\u2192 Random errors :<br \/>\nThese errors will occur irregularly. They may be positive (or) negative in sign. We cannot predict the presence of these errors.<br \/>\nEx:<\/p>\n<ul>\n<li>Voltage fluctuations of power supply<\/li>\n<li>Mechanical vibrations in experimental set up.<\/li>\n<\/ul>\n<p>\u2192 Least count error: This is a systematic error. It depends on the smallest value that can be measured by the instrument.<br \/>\nLeast count error can be minimized by using instruments of highest precision.<\/p>\n<p>\u2192 Arithmetic mean: The average value of all the measurements is taken as arithmetic mean.<br \/>\nLet the number of observations be a<sub>1<\/sub>, a<sub>2<\/sub>, a<sub>3<\/sub> &#8230;&#8230;&#8230;.. a<sub>n<\/sub><\/p>\n<p>Then the arithmetic mean<br \/>\na<sub>mean<\/sub> = \\(\\frac{\\mathbf{a}_1+\\mathbf{a}_2+\\mathbf{a}_3+\\ldots \\ldots \\ldots .+\\mathbf{a}_{\\mathbf{n}}}{\\mathbf{n}}\\)<br \/>\nor a<sub>mean<\/sub> = \\(\\sum_{i=1}^n \\frac{a_i}{n}\\)<\/p>\n<p>\u2192 Absolute error (|\u0394a|): The magnitude of the difference between the individual measurement and true value of the quantity is called absolute error of the measurement. It is denoted by |\u0394a|<br \/>\nAbsolute error<br \/>\n|\u0394a| = |a<sub>mean<\/sub> &#8211; a<sub>i<\/sub>|<br \/>\n= |True value &#8211; measured value|<\/p>\n<p>\u2192 Mean absolute error ( Aa[nrnnl: The arithmetic mean value of all absolute errors is known as mean absolute error.<br \/>\nLet \u2018n\u2019 measurements are taken, then their absolute errors are, say |\u0394a<sub>1<\/sub>|, |\u0394a<sub>2<\/sub>|, |\u0394a<sub>3<\/sub>| &#8230;&#8230;.. ||\u0394a<sub>n<\/sub>|, then<br \/>\n|\u0394a<sub>mean<\/sub>| = \\(\\frac{\\left|\\Delta a_1\\right|+\\left|\\Delta a_2\\right|+\\left|\\Delta a_3\\right|+\\ldots \\ldots \\ldots+\\left|\\Delta a_n\\right|}{n}\\)<br \/>\nor<br \/>\n\u0394a<sub>mean<\/sub> = \\(\\frac{1}{n} \\sum_{i=1}^n \\Delta a_i\\)<\/p>\n<p>\u2192 Relative error: Relative error is the ratio of the mean absolute error A amean to the mean value a mean of the quantity measure.<br \/>\nRelative error = \\(\\frac{\\Delta \\mathbf{a}_{\\text {mean }}}{\\mathbf{a}_{\\text {mean }}}\\)<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/tsboardsolutions.com\/wp-content\/uploads\/2022\/10\/TS-Board-Solutions.png\" alt=\"TS Inter 1st Year Physics Notes Chapter 2 Units and Measurements\" width=\"183\" height=\"15\" \/><\/p>\n<p>\u2192 Percentage error (\u03b4a): When relative error is expressed in percent then it is called percentage error.<br \/>\nPercentage error (\u03b4a) = \\(\\frac{\\Delta \\mathbf{a}_{\\text {mean }}}{\\mathbf{a}_{\\text {mean }}}\\) \u00d7 100<\/p>\n<p>\u2192 Significant figures: The scientific way to report a result must always have all the reliably known (measured) values plus one uncertain digit (first digit). These are known as &#8220;significant figures&#8221;.<br \/>\nThis additional digit indicates the uncertainty of measurement.<br \/>\nEx: In a measurement, the length of a body is reported as 287.5 cm. Then, in that measu-rement, the length is believable up to 287 cm<br \/>\ni. e., the digits 2, 8 and 7 are certain. The first digit (5) is uncertain. Its value may change.<\/p>\n<p>\u2192 Rules in determining significant numbers<\/p>\n<ul>\n<li>All the non-zero digits are significant.<\/li>\n<li>All the zeros in between two non-zero digits are significant.<\/li>\n<li>If the number is less than one, the zeros on the right of decimal point to the first nonzero digit are not significant.<br \/>\nEx : In a result 0.002308 the zeros before the digit \u20182\u2019 are non significant.<\/li>\n<li>The terminal or trailing zeros in a number without decimal point are not significant. Ex: In the result 123 m = 12300 cm = 123000 mm the zeros after the digit \u20183\u2019 are not significant.<\/li>\n<li>The trailing zeros in a number with a decimal point are significant.<br \/>\nEx : In the result 3.500 or 0.06900 the last zeros are significant. So number of significant figures are four in each case.<\/li>\n<\/ul>\n<p>\u2192 Rules for arithmetic operation with sig-nificant figures<br \/>\n1. In multiplication or division, the final result should retain as many significant figures as are there in the original number with the least significant figures.<br \/>\nEx : In the division \\(\\frac{4.237}{2.51}\\) the significant figures are 4 and 3, so least significant figures are \u20183\u2019.<br \/>\n\\(\\frac{4.237}{2.51}\\) = 1.69 i.e., final answer must have only \u20183\u2019 significant digits.<\/p>\n<p>2. In addition or subtraction, the final result should retain as many decimal places as are there in the number with the least decimal places.<br \/>\nEx: 436.26g + 227.2 g Here least number of significant figures after decimal point is one.<br \/>\n436.26 + 272.2 = 708.46 must be expressed as 708.5 (after rounding off the last digit).<\/p>\n<p>\u2192 Rounding off the uncertain digits Rules for rounding off procedure : In rounding off the numbers to the required number of significant digits the following rules are followed.<\/p>\n<ul>\n<li>The preceding significant digit is raised by one if the first non-significant digit is more than 5.<\/li>\n<li>The preceding significant digit is left unchanged if the first non-significant digit is less than 5.<\/li>\n<li>If the first non-significant figure is 5 then<br \/>\n(a) If the preceding significant figure is an odd number then add one to it.<br \/>\n(b) If the preceding significant figure is an even number then it is unchanged and 5 is discarded.<\/li>\n<\/ul>\n<p>\u2192 Dimension: The power of a fundamental quantity in the given derived quantity is called<br \/>\ndimension.<br \/>\nEx: Force dimensional formula MLT<sup>-2<\/sup> Here dimensions of Mass \u2192 1, Length \u2192 1, Time \u2192 2<\/p>\n<p>\u2192 Dimensional formula: It is a mathematical expression giving relation between various fundamental quantities of a derived physical quantity.<br \/>\nEx : Momentum (P),MLT<sup>-1<\/sup>,<br \/>\nEnergy ML<sup>2<\/sup>T<sup>-2<\/sup> etc.<\/p>\n<p>\u2192 Uses of dimensional methods :<\/p>\n<ul>\n<li>To convert units from one system to another system.<\/li>\n<li>To check the validity of given physical equations. For this purpose, we will use homogeneity of dimensions on L.H.S and on R.H.S.<\/li>\n<li>To derive new relations between various physical quantities.<\/li>\n<\/ul>\n<p>\u2192 Dimensional formulae of physical quantities:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35660\" src=\"https:\/\/tsboardsolutions.com\/wp-content\/uploads\/2022\/11\/TS-Inter-1st-Year-Physics-Notes-Chapter-2-Units-and-Measurements-1.png\" alt=\"TS Inter 1st Year Physics Notes Chapter 2 Units and Measurements 1\" width=\"615\" height=\"848\" srcset=\"https:\/\/tsboardsolutions.com\/wp-content\/uploads\/2022\/11\/TS-Inter-1st-Year-Physics-Notes-Chapter-2-Units-and-Measurements-1.png 615w, https:\/\/tsboardsolutions.com\/wp-content\/uploads\/2022\/11\/TS-Inter-1st-Year-Physics-Notes-Chapter-2-Units-and-Measurements-1-218x300.png 218w\" sizes=\"(max-width: 615px) 100vw, 615px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35659\" src=\"https:\/\/tsboardsolutions.com\/wp-content\/uploads\/2022\/11\/TS-Inter-1st-Year-Physics-Notes-Chapter-2-Units-and-Measurements-2.png\" alt=\"TS Inter 1st Year Physics Notes Chapter 2 Units and Measurements 2\" width=\"602\" height=\"856\" srcset=\"https:\/\/tsboardsolutions.com\/wp-content\/uploads\/2022\/11\/TS-Inter-1st-Year-Physics-Notes-Chapter-2-Units-and-Measurements-2.png 602w, https:\/\/tsboardsolutions.com\/wp-content\/uploads\/2022\/11\/TS-Inter-1st-Year-Physics-Notes-Chapter-2-Units-and-Measurements-2-211x300.png 211w\" sizes=\"(max-width: 602px) 100vw, 602px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35658\" src=\"https:\/\/tsboardsolutions.com\/wp-content\/uploads\/2022\/11\/TS-Inter-1st-Year-Physics-Notes-Chapter-2-Units-and-Measurements-3.png\" alt=\"TS Inter 1st Year Physics Notes Chapter 2 Units and Measurements 3\" width=\"604\" height=\"119\" srcset=\"https:\/\/tsboardsolutions.com\/wp-content\/uploads\/2022\/11\/TS-Inter-1st-Year-Physics-Notes-Chapter-2-Units-and-Measurements-3.png 604w, https:\/\/tsboardsolutions.com\/wp-content\/uploads\/2022\/11\/TS-Inter-1st-Year-Physics-Notes-Chapter-2-Units-and-Measurements-3-300x59.png 300w\" sizes=\"(max-width: 604px) 100vw, 604px\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here students can locate TS Inter 1st Year Physics Notes 2nd Lesson Units and Measurements to prepare for their exam. TS Inter 1st Year Physics Notes 2nd Lesson Units and Measurements \u2192 Fundamental Quantity : A fundamental quantity is one which is unique and freely existing. It does not depend on any other physical quantity. &#8230; <a title=\"TS Inter 1st Year Physics Notes Chapter 2 Units and Measurements\" class=\"read-more\" href=\"https:\/\/tsboardsolutions.com\/ts-inter-1st-year-physics-notes-chapter-2\/\" aria-label=\"More on TS Inter 1st Year Physics Notes Chapter 2 Units and Measurements\">Read more<\/a><\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[27],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v19.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>TS Inter 1st Year Physics Notes Chapter 2 Units and Measurements - TS Board Solutions<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/tsboardsolutions.com\/ts-inter-1st-year-physics-notes-chapter-2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"TS Inter 1st Year Physics Notes Chapter 2 Units and Measurements - TS Board Solutions\" \/>\n<meta property=\"og:description\" content=\"Here students can locate TS Inter 1st Year Physics Notes 2nd Lesson Units and Measurements to prepare for their exam. 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TS Inter 1st Year Physics Notes 2nd Lesson Units and Measurements \u2192 Fundamental Quantity : A fundamental quantity is one which is unique and freely existing. It does not depend on any other physical quantity. ... 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