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Physics. Phys - 1. Units And Measurements. We know an elephant is heavier than a feather. Physics wants to know by how many time, by what standards and with what accuracy. Session Opener. Session Objectives. Session Objective. Standard and Units. Dimensions. Dimensional Analysis.
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Phys - 1 Units And Measurements
We know an elephant is heavier than a feather Physics wants to know by how many time, by what standards and with what accuracy. Session Opener
Session Objective Standard and Units Dimensions Dimensional Analysis Errors Significant Figures Accuracy and Precision
Standards and Units Laws of physics : expressed in terms of physical quantities Physical quantities : expressed in terms of fundamental quantities. Fundamental quantities : defined by measurements and expressed by standards. Measurements : comparison with a standard. Standards are defined and universally accepted by competent authority.
Standards and Units Physical quantity (q) given by a number and a unit. q = n . u n : pure number. u : unit of the standard. Because q is the same whatever be the standard
Number of times a fundamental quantity is repeated in physical quantity q Area is 2 dimensional in length b c a Volume is 3 dimensional in length Dimensions of physical quantities
Dimension • Quantities with same dimensions only can be added • Power of dimension on both sides of an equation must match
Class Exercise - 7 Dimensionally, specific heat is proportional to dimension of mass as • [M0] (b) [M1] • (c) [M–1] (d) [M2]
Solution - 7 Specific heat is (dimensionally) Heat (energy) per unit mass per unit temperature (q) Then,
Dimensional Analysis Dimensional analysis is a powerful method For interconversion of units To test whether a relation is wrong. To justify /derive interrelation of quantities.
Class Exercise - 8 Show dimensionally which of the following physical quantities have an influence on the time period of a simple pendulum? (i) Mass of the bob (ii) Length of the string (l) (iii) Acceleration due to gravity (g) and (iv) Angular displacement (q)
Solution - 8 Time period = T Then Relation with q cannot be found dimensionally.
Class Exercise - 9 What is the value of a force of 10 N in a system with fundamental units of centimetre, gram and hour?
Solution - 9 • q = n1u1 = n2u2 • 10 N = n2 new unit = 106 × 60 × 60 = 3.6 × 109
Class Exercise - 10 Check dimensionally if the relation is correct.
Solution - 10 Dimension of left-hand side (s) = [M0L1T0] On right-hand side: ut = Velocity × Time = [M0L1T–1][T] = [M0L1T0] same as LHS = [M0L1T0] [Same as LHS] Equation is dimensionally correct.
Measured value qm = qreal q Exact value of qreal is not known Only mean value of q can be found Errors An observation is limited by the least count of instrument
Errors Random errors are expected when several observations (qi) are made
In sums and differences, ABSOLUTE ERRORS are added A B = C C C = A B ( A + B) Errors In products or quotients,RELATIVE ERRORS are added
Class Exercise - 3 The percentage errors of X, Y, X are x, y and z respectively. The total percentage error in the product XYZ is (a) xyz (b) x + y + z Solution :- b Percentage errors are added in a product.
Class Exercise - 6 The least count of a stop watch is 0.2 s. The time of 20 oscillations of a pendulum is measured to be 25 s. The percentage error in the measurement of time is • 8% (b) 1.8% • (c) 0.8% (d) 0.1% Solution Total time measured is important and not time period. So percentage error
Accuracy and Precision (i) Accuracy Accuracy : degree of agreement of a measurement with the true (accepted) value. Sign has to be retained while expressing accuracy. (ii) Precision Precision : degree of agreement between two or more measurements done in an identical manner. Precision is expressed without any sign.
Significant figures Significant figures are the meaningful digits in a measured or calculated quantity. Significant figures in 1.007,12.012 and 10.070 are 4, 5 and 5 respectively.
Rules to determine significant figures • All non-zero digits are significant. • Zeroes to the left of the first non-zero • digit are not significant. iii. Zeroes between non-zero digits are significant. • iv Zeroes to the right of the decimal point are • significant.
Class Exercise - 2 Which of the following, in the measurement of length, is most accurate? (a) 2 × 102m (b) 200.0 m (c) 20 × 102 m (d) 200 m Solution :- 200.0 has four significant figures, which is maximum in the group.
Class Exercise - 5 Which of the following measurements is most precise? (a) 2345 m (b) 234.5 m (c) 23.45 m (d) 2.345 m Solution - d 2.345 m measures till the smallest fraction of a meter.
Class Exercise - 4 With regard to the significant figures, (12.5)2 is equal to (a) 156.250 (b) 156.25 (c) 156.2 (d) 156 Solution (12.5)2 = 156.25. But as only three significant figures are to be considered, 156 is the right answer.
Class Exercise - 1 Which of the following statements is false among the statements given below? (a) All non-zero digits are significant. (b) Zeroes in the middle of a numerical expression are significant, while those immediately following a decimal point are not. (c) While counting the number of significant figures, the powers of 10 are to be considered. (d) Greater the number of significant figures in a measurement, smaller is the percentage error.
Solution - 1 Ans. c In powers of 10 placed as: 212.2 = 2.122 × 102,,102 is not significant.
