class 11 notes

Class 11 Physics Notes Chapter 1 (Chapter 1) – Lab Manual (English) Book

Philoid

Philoid

— 7 min read

Lab Manual (English)
Alright class, let's delve into Chapter 1 of your Physics Lab Manual. This chapter lays the groundwork for all experimental work by focusing on the essential concepts of measurement, units, errors, and dimensions. Understanding these fundamentals is crucial not just for your practicals but also forms a significant part of the syllabus for various government exams.

Chapter 1: Introduction (Units, Measurements, Errors, Dimensions)

1. Physics and Measurement:

  • Physics is a quantitative science, relying heavily on precise measurement of physical quantities.
  • Physical Quantity: Any quantity that can be measured (e.g., length, mass, time, force, temperature).
  • Measurement: The comparison of an unknown physical quantity with a known, fixed standard quantity of the same nature, called a unit.
  • Measurement = Numerical Value (n) × Unit (u)

2. System of Units:

  • A complete set of fundamental and derived units for all kinds of physical quantities.
  • Common Systems:
    • CGS: Centimetre, Gram, Second
    • FPS: Foot, Pound, Second
    • MKS: Metre, Kilogram, Second
    • SI (Système Internationale d'Unités): The internationally accepted system, a rationalized and extended version of the MKS system.

3. SI System:

  • Fundamental (or Base) Quantities and Units: There are 7 fundamental quantities in SI.

    S.No. Fundamental Quantity SI Unit Symbol
    1 Length metre m
    2 Mass kilogram kg
    3 Time second s
    4 Electric Current ampere A
    5 Temperature kelvin K
    6 Amount of Substance mole mol
    7 Luminous Intensity candela cd

  • Supplementary Units:

    • Plane Angle: radian (rad)
    • Solid Angle: steradian (sr)

  • Derived Units: Units of physical quantities that can be expressed in terms of fundamental units (e.g., velocity (m/s), acceleration (m/s²), force (kg m/s² or Newton), work (kg m²/s² or Joule)).

4. Measurement of Length:

  • Direct Methods: Using instruments like metre scale (Least Count: 1 mm), Vernier Callipers (LC: typically 0.1 mm or 0.01 cm), Screw Gauge/Micrometer (LC: typically 0.01 mm or 0.001 cm).
  • Least Count (LC): The smallest measurement that can be made accurately using an instrument.
    • Vernier Callipers LC: Value of 1 Main Scale Division (MSD) - Value of 1 Vernier Scale Division (VSD). Often calculated as (Value of 1 MSD) / (Total number of VSD).
    • Screw Gauge LC: (Pitch) / (Total number of divisions on the circular scale).
      • Pitch: Distance moved by the screw for one complete rotation of the circular scale (usually 1 mm or 0.5 mm).
  • Zero Error & Correction: Instruments like Vernier Callipers and Screw Gauge may have zero error (positive or negative) if the zero of the Vernier/Circular scale doesn't coincide with the main scale zero when the jaws/studs are in contact.
    • Correct Reading = Observed Reading - Zero Error (with sign).

5. Errors in Measurement:

  • The uncertainty in the measurement of a physical quantity.

  • Accuracy: How close the measured value is to the true value.

  • Precision: The resolution or limit to which the quantity is measured (related to the least count of the instrument).

  • Types of Errors:

    • Systematic Errors: Errors that tend to be in one direction (positive or negative). Causes:
      • Instrumental errors (e.g., zero error, faulty calibration).
      • Imperfection in experimental technique/procedure.
      • Personal errors (e.g., parallax error, bias).
      • External causes (e.g., changes in temperature, pressure).
      • Can be minimized by improving techniques, using better instruments, and applying corrections.
    • Random Errors: Irregular errors occurring due to unpredictable fluctuations. Can be positive or negative.
      • Can be minimized by repeating the observation several times and taking the arithmetic mean.

  • Calculating Errors:

    • Let measurements be a₁, a₂, ..., aₙ.
    • True Value (approx): Arithmetic Mean, a_mean = (a₁ + a₂ + ... + aₙ) / n
    • Absolute Error: Magnitude of the difference between the true value and the individual measured value.
      • Δa₁ = |a_mean - a₁|, Δa₂ = |a_mean - a₂|, ...
    • Mean Absolute Error: Arithmetic mean of the absolute errors.
      • Δa_mean = (Δa₁ + Δa₂ + ... + Δaₙ) / n
      • Final result expressed as: a = a_mean ± Δa_mean
    • Relative Error: Ratio of mean absolute error to the mean value.
      • Relative Error = Δa_mean / a_mean
    • Percentage Error: Relative error expressed as a percentage.
      • Percentage Error = (Δa_mean / a_mean) × 100%

  • Combination of Errors:

    • Addition/Subtraction: If Z = A ± B, then ΔZ = ΔA + ΔB (Absolute errors add up).
    • Multiplication/Division: If Z = A × B or Z = A / B, then ΔZ/Z = ΔA/A + ΔB/B (Relative errors add up).
    • Power: If Z = Aⁿ, then ΔZ/Z = n (ΔA/A).

6. Significant Figures:

  • Digits in a measured value that are known reliably plus one uncertain digit. They indicate the precision of measurement.
  • Rules for Counting Significant Figures:
    1. All non-zero digits are significant. (e.g., 285 has 3 SF)
    2. All zeros between two non-zero digits are significant. (e.g., 2005 has 4 SF)
    3. If the number is less than 1, zeros on the right of the decimal point but to the left of the first non-zero digit are not significant. (e.g., 0.0052 has 2 SF)
    4. Terminal or trailing zeros in a number without a decimal point are not significant (unless specified by measurement). (e.g., 12300 m may have 3, 4, or 5 SF; better written in scientific notation like 1.23 x 10⁴ (3 SF), 1.230 x 10⁴ (4 SF), 1.2300 x 10⁴ (5 SF)).
    5. Trailing zeros in a number with a decimal point are significant. (e.g., 3.500 has 4 SF; 0.06900 has 4 SF)
  • Rules for Arithmetic Operations:
    1. Multiplication/Division: The final result should retain as many significant figures as there are in the original number with the least significant figures.
    2. Addition/Subtraction: The final result should retain as many decimal places as there are in the number with the least decimal places.
  • Rounding Off:
    1. If the insignificant digit to be dropped is > 5, precede it by increasing the preceding digit by 1.
    2. If the insignificant digit to be dropped is < 5, leave the preceding digit unchanged.
    3. If the insignificant digit to be dropped is = 5, and the preceding digit is even, leave it unchanged. If the preceding digit is odd, increase it by 1. (This avoids bias in rounding).

7. Dimensions of Physical Quantities:

  • The powers to which the fundamental units (like Mass [M], Length [L], Time [T], etc.) must be raised to represent that quantity.
  • Dimensional Formula: An expression showing how and which fundamental quantities represent the dimensions of a physical quantity. (e.g., Velocity = [M⁰ L¹ T⁻¹], Force = [M¹ L¹ T⁻²])
  • Dimensional Equation: An equation obtained by equating a physical quantity with its dimensional formula. (e.g., [F] = [M L T⁻²])

8. Dimensional Analysis and its Applications:

  • Principle of Homogeneity: Dimensions of all terms on both sides of a physical equation must be the same.
  • Applications:
    1. Checking Dimensional Consistency: Verify if an equation is dimensionally correct. (Note: A dimensionally correct equation may not be physically correct, but a dimensionally incorrect equation must be wrong).
    2. Deducing Relations: Establishing relations among physical quantities (if the dependence is known, usually product type).
    3. Converting Units: Converting a physical quantity from one system of units to another (using n₁u₁ = n₂u₂).
  • Limitations:
    1. Cannot determine dimensionless constants.
    2. Cannot be used for equations involving trigonometric, logarithmic, or exponential functions.
    3. Cannot derive relations involving more than 3 fundamental quantities (if only M, L, T are involved).
    4. Fails if the relation involves addition or subtraction of quantities.

Multiple Choice Questions (MCQs):

  1. The SI unit of luminous intensity is:
    (a) lumen
    (b) lux
    (c) candela
    (d) watt/sr

  2. A screw gauge has a least count of 0.01 mm and there are 50 divisions on the circular scale. The pitch of the screw gauge is:
    (a) 0.25 mm
    (b) 0.5 mm
    (c) 1.0 mm
    (d) 0.01 mm

  3. The number of significant figures in the measurement 0.070800 m is:
    (a) 3
    (b) 4
    (c) 5
    (d) 6

  4. If the length and breadth of a rectangle are measured as (5.7 ± 0.1) cm and (3.4 ± 0.2) cm, respectively, the percentage error in the area is approximately:
    (a) 1.8%
    (b) 5.9%
    (c) 7.7%
    (d) 0.3%

  5. The dimensional formula for Gravitational Constant (G) is: (Hint: Use F = G m₁m₂ / r²)
    (a) [M⁻¹ L³ T⁻²]
    (b) [M¹ L³ T⁻²]
    (c) [M⁻¹ L⁻³ T²]
    (d) [M¹ L⁻³ T²]

  6. Which of the following pairs does not have the same dimensions?
    (a) Work and Torque
    (b) Angular Momentum and Planck's Constant
    (c) Impulse and Momentum
    (d) Force and Pressure

  7. The density of a material in the CGS system is 4 g/cm³. In a system of units where the unit of length is 10 cm and the unit of mass is 100 g, the value of density will be:
    (a) 0.4
    (b) 40
    (c) 400
    (d) 0.04

  8. Which type of error can be minimized by taking multiple readings and calculating the mean?
    (a) Systematic Error
    (b) Instrumental Error
    (c) Personal Error
    (d) Random Error

  9. According to the principle of homogeneity of dimensions, which of the following is correct?
    (a) An equation must be physically correct if it is dimensionally correct.
    (b) Quantities with different dimensions can be added.
    (c) Dimensions of all terms in a physical equation must be identical.
    (d) Dimensional analysis can determine the value of dimensionless constants.

  10. A vernier callipers has 10 VSD coinciding with 9 MSD. If one MSD is 1 mm, the least count of the instrument is:
    (a) 1 mm
    (b) 0.1 mm
    (c) 0.01 mm
    (d) 0.9 mm

Answer Key for MCQs:

  1. (c)
  2. (b) [LC = Pitch / No. of div => Pitch = LC * No. of div = 0.01 mm * 50 = 0.5 mm]
  3. (c) [Non-zero 7, 8 are SF. Zero between them is SF. Trailing zeros after decimal are SF. Initial zeros are not.]
  4. (c) [%Error in L = (0.1/5.7)*100 ≈ 1.75%; %Error in B = (0.2/3.4)*100 ≈ 5.88%; %Error in Area = %Error in L + %Error in B ≈ 1.75 + 5.88 ≈ 7.63%]
  5. (a) [G = F r² / (m₁m₂) => [G] = [MLT⁻²][L²] / [M][M] = [M⁻¹ L³ T⁻²]]
  6. (d) [Force = MLT⁻², Pressure = Force/Area = MLT⁻²/L² = ML⁻¹T⁻²]
  7. (b) [Density = Mass/Volume. n₂ = n₁ [M₁/M₂]¹ [L₁/L₂]⁻³. n₁=4, M₁=g, M₂=100g, L₁=cm, L₂=10cm. n₂ = 4 [g/100g]¹ [cm/10cm]⁻³ = 4 * (1/100) * (1/10)⁻³ = 4 * (1/100) * 1000 = 40]
  8. (d)
  9. (c)
  10. (b) [LC = 1 MSD - 1 VSD. Given 10 VSD = 9 MSD => 1 VSD = 9/10 MSD = 0.9 MSD. LC = 1 MSD - 0.9 MSD = 0.1 MSD. Since 1 MSD = 1 mm, LC = 0.1 mm]

Make sure you revise these concepts thoroughly. Pay special attention to SI units, dimensional formulae of common quantities, rules for significant figures, and calculation of least count and percentage error. Good luck with your preparation!

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