• Like
  • Save

Loading…

Flash Player 9 (or above) is needed to view presentations.
We have detected that you do not have it on your computer. To install it, go here.

Units and Measurement

  • 3,076 views
Uploaded on

Session of Units and Dimensions for Arc-IITJEE study program

Session of Units and Dimensions for Arc-IITJEE study program

More in: Technology , Education
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Be the first to comment
No Downloads

Views

Total Views
3,076
On Slideshare
0
From Embeds
0
Number of Embeds
1

Actions

Shares
Downloads
0
Comments
0
Likes
7

Embeds 0

No embeds

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
    No notes for slide

Transcript

  • 1. Physics
  • 2. Phys - 1 Units And Measurements
  • 3. Session Opener We know an elephant is heavier than a feather Physics wants to know by how many time, by what standards and with what accuracy.
  • 4. Session Objectives
  • 5. Session Objective Standard and Units Dimensions Errors Significant Figures Accuracy and Precision Dimensional Analysis
  • 6. 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.
  • 7. 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
  • 8. SI (International system) units mol Mole Amount of substance 7. cd Candela Luminous intensity 6. K Kelvin Temperature 5. A Ampere Electric current 4. s Second Time 3. kg Kilogram Mass 2. m Meter Length 1. Symbol of SI unit Name of SI unit Basic physical quantity
  • 9. Dimensions of physical quantities Number of times a fundamental quantity is repeated in physical quantity q Volume is 3 dimensional in length Area is 2 dimensional in length a b c
  • 10. Dimension • Quantities with same dimensions only can be added • Power of dimension on both sides of an equation must match
  • 11. Questions
  • 12. Class Exercise - 7 Dimensionally, specific heat is proportional to dimension of mass as
    • [M 0 ] (b) [M 1 ]
    • (c) [M –1 ] (d) [M 2 ]
  • 13. Solution - 7 Specific heat is (dimensionally) Heat (energy) per unit mass per unit temperature (q) Then,
  • 14. Dimensional Analysis To test whether a relation is wrong. For interconversion of units To justify /derive interrelation of quantities. Dimensional analysis is a powerful method
  • 15. Questions
  • 16. 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 (  )
  • 17. Solution - 8 Time period = T Then Relation with  cannot be found dimensionally.
  • 18. Class Exercise - 9 What is the value of a force of 10 N in a system with fundamental units of centimetre, gram and hour?
  • 19. Solution - 9
        • q = n 1 u 1 = n 2 u 2
    • 10 N = n 2 new unit
    = 10 6 × 60 × 60 = 3.6 × 10 9
  • 20. Class Exercise - 10 Check dimensionally if the relation is correct.
  • 21. Solution - 10 Dimension of left-hand side (s) = [M 0 L 1 T 0 ] On right-hand side: ut = Velocity × Time = [M 0 L 1 T –1 ][T] = [M 0 L 1 T 0 ] same as LHS = [M 0 L 1 T 0 ] [Same as LHS] Equation is dimensionally correct.
  • 22. Errors An observation is limited by the least count of instrument Measured value q m = q real   q Exact value of q real is not known Only mean value of q can be found
  • 23. Errors Random errors are expected when several observations (q i ) are made
  • 24. Errors In products or quotients, RELATIVE ERRORS are added In sums and differences, ABSOLUTE ERRORS are added A  B = C C   C = A  B  (  A +  B)
  • 25. Questions
  • 26. 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 Percentage errors are added in a product. Solution :- b
  • 27. 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
  • 28. Accuracy and Precision (i) Accuracy Sign has to be retained while expressing accuracy. Accuracy : degree of agreement of a measurement with the true (accepted) value. (ii) Precision Precision is expressed without any sign. Precision : degree of agreement between two or more measurements done in an identical manner.
  • 29. Significant figures Significant figures in 1.007, 12.012 and 10.070 are 4, 5 and 5 respectively. Significant figures are the meaningful digits in a measured or calculated quantity.
  • 30. Rules to determine significant figures
    • All non-zero digits are significant.
    • iv Zeroes to the right of the decimal point are
      • significant.
    iii. Zeroes between non-zero digits are significant.
    • Zeroes to the left of the first non-zero
    • digit are not significant.
  • 31. Questions
  • 32. Class Exercise - 2 Which of the following, in the measurement of length, is most accurate? (a) 2 × 10 2 m (b) 200.0 m (c) 20 × 10 2 m (d) 200 m 200.0 has four significant figures, which is maximum in the group. Solution :-
  • 33. 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.
  • 34. 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 (12.5) 2 = 156.25. But as only three significant figures are to be considered, 156 is the right answer. Solution
  • 35. 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.
  • 36. Solution - 1 In powers of 10 placed as: 212.2 = 2.122 × 10 2 , , 10 2 is not significant. Ans. c
  • 37. Thank you