Title Med-RM_Phy_SP-1_Ch-2_Units and Measurement.pdf ✅

8 Units and Measurement NEET Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456 The SI unit is based on the following seven fundamental units and two supplementary units : Sl. No. Fundamental Quantity Fundamental Unit Unit Symbol Used 1. Mass kilogram kg 2. Length metre m 3. Time second s 4. Temperature kelvin K 5. Electric current ampere A 6. Luminous Intensity candela cd 7. Amount of Matter mole mol Sl. No. Supplementary Supplementary Unit Symbol Physical Quantity Unit Used 1. Plane angle Radian rad 2. Solid angle Steradian sr Note : (i) Unit cannot be plural e.g., writing 5 kgs is wrong, the correct is 5 kg. (ii) If the name of a unit is the name of a scientist and you are writing the complete name start from small letter, e.g., 5 ampere and if you are writing the single letter use capital letter, e.g., 5 A. B. Derived Unit If the unit of a physical quantity depends on the units of the fundamental quantities then the quantity is said to be dependent physical quantity (derived quantity) and its unit is dependent unit or (derived unit). e.g. unit of velocity is m/s, which depends on the unit of length and time and hence the velocity is said to be dependent quantity and its unit as derived unit. METRIC PREFIXES FOR POWERS OF 10 : The physical quantities whose magnitude is either too large or too small can be expressed more compactly by the use of certain prefixes as given in the table. TABLE : METRIC PREFIXES Power of 10 Prefix Symbol Power of 10 Prefix Symbol 10 deci d 10 deca da 10 centi c 10 hecto h 10 milli m 10 kilo k 10 micro μ 10 mega M 10 nano n 10 giga G 10 pico p 10 tera T 10 femto f 10 peta P 10 atto a 10 exa E –1 1 –2 2 –3 3 –6 6 –9 9 –12 12 –15 15 –18 18 ORDER OF MAGNITUDE If the magnitude of a physical quantity is expressed as a × 10b, where (a 5), then the exponent b is called the order of magnitude of the physical quantity. If 5 < a  10, then the order of magnitude of the physical quantity become b + 1, where b is any positive or negative exponent (or power) of 10. For example, the speed of light is given as 3.00 × 108 m s–1. So the order of magnitude of the speed of light is 8. The order of magnitude, gives an estimate of the magnitude of the quantity. The charge on an electron is 1.6 × 10–19 C. Therefore, we can say that the charge possessed by an electron is of the order 10–19 or its order of magnitude is – 19. The expression of a quantity as a × 10b is called scientific notation.
NEET Units and Measurement 9 Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456 ACCURACY, PRECISION OF INSTRUMENTS Accuracy : It is a measure of how close the measured value is to the true value of the quantity. It may depend on many factors. As we reduce the errors, the measurement becomes more accurate. Let the true value of a quantity is 3.9 and its measurements taken by two boys are 3.6 and 3.8. Here 3.8 is more accurate as it is closer to the true value. Precision : It tells us as to what resolution or limit, the quantity is measured. It mainly depends on least count of instrument. If we measure a certain thickness by two different devices having resolutions 0.1 cm (a metre scale) and 0.01 cm (a vernier callipers), the latter will give a measurement having more precision. Thus a value 1.56 is more precise than 1.5. It is not necessary that a more precise value is more accurate too. Let a man measure a length of 5.65 cm by the above mentioned two devices, and obtains the values 5.5 cm and 5.34 cm respectively. Though the first value is less precise, it is more accurate as it is closer to the true value. And 5.34 cm is less accurate but more precise. Example 1 : The true value of a particular length is 4.283 cm. The three instruments A, B and C, used to measure this length give the readings 4.1 cm, 4.24 cm and 4.093 cm. Arrange these readings in the increasing order of accuracy and precision. Which instrument is most reliable for measuring this length? Solution : True value = 4.283 cm Closer the measured value to its true value, more accurate is the reading. Hence, the three readings can be arranged in increasing order of accuracy as 4.093 cm < 4.1 cm < 4.24 cm. The reading of the instrument B is most accurate. In the increasing order of precision, the readings are 4.1 cm < 4.24 cm < 4.093 cm The instrument C provides the reading upto greatest precision. But since its accuracy is least, it cannot be considered reliable. In terms of accuracy and precision both, instrument B is best suited to take the measurements. ERRORS IN MEASUREMENT The difference of true value and measured value is called error in measurement. Error = Measured value – True value Various Types of Error (1) Systematic error: This error occur only in one direction, i.e. either positive or negative. This error arise due to following reasons (i) Instrumental errors Improper designing or calibration Least count of instrument Zero error (ii) Imperfection in experimental technique (iii) Variation in experimental condition: Like change in temperature, wind speed, humidity etc. (iv) Personal error: Error due to carelessness or casual behaviour.
10 Units and Measurement NEET Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456 (2) Random error: The error which cannot be associated with any constant cause called random error. This error can randomly have any sign i.e. positive or negative. These errors can be minimised by taking large number of observation. If the number of observation increase by n times then random error decrease by n times. Calculation of Errors (i) True value: The arithmatic mean of measured values called true value. If measured values are a1, a2, a3, ..... an 12 3 ... True value n m aa a a a n   (ii) Absolute Error : Magnitude of difference of true value and measured value called absolute error       1 1 2 2 | || | | || | ............................ ............................ | || | m m n mn a aa a aa a aa (iii) Mean Absolute Error :       1 2 ...... aa an a n Final result of measurement may be written as : a = am ± a (iv) Relative Error or Fractional Error : Mean absolute error m Mean value of measurement a a    (v) Percentage Error   100% m a a Combination of Errors : A. In sum and Difference When physical quantities are added or subtract then the maximum absolute error in the result is the sum of the absolute errors of the individual quantities. (i) In Sum : If Z = A + B, then Maximum absolute error Z = A + B, Maximum fractional error       ZA B Z AB AB (ii) In Difference : If Z = A – B, then maximum absolute error is Z = A + B Maximum fractional error in this case       ZA B Z AB AB