Tiêu đề 2. Units And Measurements.pdf ✅

Å All the quantities which are used to describe the laws of physics are called physical quantities, e.g. length, mass, volume, etc. Å Physical quantities are of two types, first is fundamental quantities which are independent of other physical quantities and second is derived quantities which can be derived from the fundamental quantities. Units Å Measurement of any physical quantity involves comparison with a certain basic, arbitrarily chosen, internationally accepted reference standard called unit. Å The units which are used to represent fundamental quantities are called fundamental or base units. However, the unit of derived quantities which are represented in terms of fundamental units are called derived units. Å Some of the commonly used systems of units for measurement with the base units for length, mass and time are given as (i) CGS system (Centimetre, Gram and Second, respectively) (ii) FPS system (Foot, Pound and Second, respectively) (iii) MKS system (Metre, Kilogram and Second, respectively) International System of Units (SI) Å The system of units which is at present internationally accepted for measurement is the international system of units. Å This system contains 7 fundamental units and 2 supplementary units which are tabulated as follows. Fundamental units Fundamental quantity Fundamental unit Symbol Length metre m Mass kilogram kg Time second s Electric current ampere A Temperature kelvin K Luminous intensity candela cd Amount of substance mole mol Supplementary units Supplementary quantity Supplementary unit Symbol Plane angle radian rad Solid angle steradian sr Units and Measurements CHAPTER >02 KEY NOTES
Measurement of Length Å There are two methods for the measurement of length as follows. (i) Direct Method In this method, measurement of length involves the use of (a) a metre scale (10−3 to 102 m) (b) Vernier callipers (upto 10−4 m) (c) screw gauge and spherometer (upto 10−5 m) (ii) Indirect Method This method is used to measure large distances such as the distance of planet or a star from the earth. e.g Parallax method, etc. Å The apparent shift in the position of an object with respect to another when we shift our eye sidewise is called parallax. The distance between two points of observation is called the basis. Å While measuring the distance D of a far away planet S by the parallax method observing from two different positions ( A and B) as shown below We get, D b = θ , where θ is called the parallax angle or parallactic angle. Å Some special units of length for measurement of short lengths are as follows 1 fermi ( )f = − 10 15 m 1 angstrom ( )Å = − 10 10 m Å Some special units of length for measurement of large lengths are as follows 1 astronomical unit (1 AU) = × 1 496 1011 . m 1 light year (ly) = × 9 46 1015 . m 1 parsec = × 3 08 1016 . m Measurement of Mass Å For measuring mass of atoms and molecules, we use unified atomic mass unit (u), where 1 atomic mass unit (u) = × − 1 66 10 27 . kg Other units that are used for measuring mass are (i) Pound = 0 4536. kg (ii) Slug = 1459. kg Å Large masses in universe like planets, stars, etc. based on Newton’s law of gravitation can be measured by using gravitational method. Å Small masses of atomic/subatomic particles, etc. can be measured by the use of mass spectrograph. Measurement of Time Å To measure any time interval, we use atomic standard of time, which is based on the periodic vibrations produced in a cesium atom. This is the basis of the cesium clock, called atomic clock. Å This clock has very high accuracy of part in 103 . Accuracy, Precision of Instruments and Errors of Measurement Å The accuracy of a measurement is a measure of how close the measured value is to the true value, while precision tells us to what resolution the quantity is measured. Å Difference in the true value and the measured value of a quantity is called error of measurement. Å The errors in measurement can be broadly classified as systematic and random errors (i) The systematic errors are those errors that tend to be in one direction, either positive or negative. Some sources of systematic errors are given as (a) Instrumental Errors It arises due to imperfect design or calibration of the measuring instrument. (b) Imperfection in Experimental Technique or Procedure It occurs due to external conditions such as change in temperature, humidity, wind velocity, pressure, etc. during experiment. (c) Personal Errors It arises due to an individual’s bias, lack of proper setting of the apparatus or individual’s carelessness in taking observations without observing proper precautions. (ii) The random errors are those errors which occur irregularly and hence are random with respect to sign. Å The least count error is the error associated with the resolution of the instrument. It occurs with both random and systematic errors. KEY NOTES S D D A b B θ

CHAPTER 02 >Units and Measurements 13 Å Rules for arithmetic operations with significant figures are as follows (i) 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. (ii) In addition or subtraction, the final result should retain as many decimal places as are there in the number with the least decimal places. Rounding Off Å The process of omitting the non-significant digits and retaining only the desired number of significant digits, in corporating the required modifications to the last significant digit is called rounding off the number. Å Rules for rounding off a measurement (i) If the number lying to the right of cut-off digit is less than 5, then the cut-off digit is retained as such. However, if it is more than 5, then the cut-off digits is increased by 1. e.g. x = 5 34. is rounded off to 5 3. to two significant digits and x = 5 328. is rounded off to 5 33. to three significant digits. (ii) If the insignificant digit to be dropped is 5, then the rule is (a) If the preceding digit is even, the insignificant digit is simply dropped, e.g. x = 6 265. is rounded off to to x = 6 26. to three significant digits. (b) If the preceding digit is odd, the preceding digit is raised by 1. e.g. x = 6 275. is rounded off to x = 6 28. to three significant digits. Å Rules for determining the uncertainty in the results of arithmetic calculations (i) If a set of experimental data is specified to n-significant figures, a result obtained by combining the data will also be valid to n-significant figures. (ii) The relative error of a value of number specified to significant figures depend not only on number of significant figures but also on the number itself. (iii) Intermediate results in a multi-step computation should be calculated to one and more significant figures in every measurement than the number of digits in the least precise measurement. Dimensions Analysis Å Dimensions of any physical quantity are those powers which are raised on fundamental units to express the unit of that physical quantity. Å Dimensional symbols of seven fundamental quantities are given as Length → [L], Mass → [M], Time → [T], Electric current → [A], Temperature → [K], Luminous intensity → [cd], Amount of substance → [mol]. Å Dimensional formula of a physical quantity is an expression which shows how and which of the fundamental quantities represent the dimensions. Å An equation obtained by equating a physical quantity with its dimensional formula is called the dimensional equation of the physical quantity. Å Principle of Homogeneity of Dimensions Only those physical quantities can be added or subtracted which have same dimensions. Å Applications of dimensions (i) To check the correctness of any physical quantity. (ii) To convert any physical quantity from one system of units to another system of units. n u n u 1 1 2 2 = where, n1 & n2 are the magnitudes and u1 & u2 are the units of any physical quantity in two systems of units. (iii) To find a relation between interdependent physical quantities.