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Physical World & Measurement

Units, dimensions, significant figures and error analysis

Key Concepts
  • SI base units: metre, kilogram, second, ampere, kelvin, mole, candela
  • Dimensional analysis: used to check equations and derive relations
  • Significant figures: reflect precision of a measurement
  • Types of error: systematic, random, gross; absolute, relative, percentage
  • Least count of an instrument limits measurement precision
Important Formulae
Percentage error ΔA/A × 100%
Error in product/quotient (A·B or A/B) ΔZ/Z = ΔA/A + ΔB/B
Error in power (Aⁿ) ΔZ/Z = n · ΔA/A
Dimensional formula of force [MLT⁻²]
Dimensional formula of energy [ML²T⁻²]
Quick Tips
  • Dimensionally incorrect equations are always wrong, but dimensionally correct ones may still be wrong (missing dimensionless constants).
  • Errors add for sums and differences; fractional errors add for products and quotients.
  • Round off: if the digit after the last significant figure is 5 and the preceding digit is odd, round up; if even, round down.
Sample Practice Questions

  1. Which physical quantity has the same dimension as that of Planck's constant?

    • Linear momentum
    • Angular momentum
    • Energy
    • Power
    Show answer

    Answer: Angular momentum

  2. In the formula X = 3YZ², the dimensions of X and Z are the same. What are the dimensions of Y?

    • M⁻¹L⁻²T⁴A²
    • ML²T⁻²
    • MLT⁻²
    • M⁻¹LT⁻²
    Show answer

    Answer: M⁻¹L⁻²T⁴A²

  3. The dimensional formula of electric field intensity E is:

    • MLT⁻²A⁻¹
    • MLT⁻³A⁻¹
    • ML²T⁻³A⁻¹
    • MLT⁻²A⁻²
    Show answer

    Answer: MLT⁻³A⁻¹

  4. In a screw gauge, pitch is 0.5 mm and circular scale has 50 divisions. Its least count is:

    • 0.5 mm
    • 0.1 mm
    • 0.01 mm
    • 0.001 mm
    Show answer

    Answer: 0.01 mm

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Practice Questions

Practice 20 randomly selected NEET questions on Physical World & Measurement. Answers are revealed after each question.

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