Units and Measurements – Class 11 Physics
By Kesari Madam | Last updated: June 2024
This comprehensive guide covers all concepts of the “Units and Measurements” chapter from Class 11 Physics syllabus, including fundamental and derived units, dimensional analysis, measurement techniques, errors, and significant figures.
1.1 Introduction to Units and Measurements
Physics is a quantitative science where we measure various physical quantities during experiments. A measurement always involves comparison with a standard measuring unit which is internationally accepted.
Kesari Madam’s Tip: Always write units when recording measurements. A number without unit is meaningless in physics!
1.2 Systems of Units
Various systems of units have been used historically:
- CGS: Centimetre-Gram-Second system
- MKS: Metre-Kilogram-Second system
- FPS: Foot-Pound-Second system
- SI: International System (modern standard)
1.2.1 Fundamental Quantities and Units
There are seven fundamental quantities in physics:
| Fundamental Quantity | SI Unit | Symbol |
|---|---|---|
| Length | metre | m |
| Mass | kilogram | kg |
| Time | second | s |
| Temperature | kelvin | K |
| Electric Current | ampere | A |
| Luminous Intensity | candela | cd |
| Amount of Substance | mole | mol |
1.2.2 Derived Quantities and Units
Quantities derived from fundamental quantities:
Momentum = mass × velocity → Unit: kg m/s or kg m s-1
1.3 Measurement of Length
The SI unit of length is the metre (m). Modern definition:
1 metre = length of path travelled by light in vacuum in 1/299,792,458 second
1.3.1 Parallax Method for Large Distances
Used to measure distances to planets and stars:
1.4 Measurement of Mass
SI unit: kilogram (kg). Modern definition based on Planck constant.
1.5 Measurement of Time
SI unit: second (s). Defined using cesium atomic clock:
1.6 Dimensions and Dimensional Analysis
Dimensions represent the physical nature of a quantity:
Velocity = [L1M0T-1]
Force = [L1M1T-2]
1.6.1 Uses of Dimensional Analysis
- Checking correctness of equations
- Deriving relationships between quantities
- Converting units between systems
1.7 Accuracy, Precision and Errors
Accuracy: Closeness to true value
Precision: Reproducibility of measurements
1.7.1 Types of Errors
- Systematic errors: Consistent offset (instrumental, observational)
- Random errors: Unpredictable variations
1.8 Significant Figures
Rules for significant figures:
- All non-zero digits are significant
- Zeros between non-zero digits are significant
- Leading zeros are not significant
- Trailing zeros after decimal are significant
Kesari Madam’s Practice Tip: When doing calculations, keep at least one extra significant figure than required in intermediate steps, and round off only the final answer.
Key Formulas
• Propagation of errors in multiplication: ΔZ/Z = ΔA/A + ΔB/B
• Propagation of errors in powers: ΔZ/Z = n(ΔA/A)
• Parallax distance: D = b/θ (θ in radians)
Exam Focus: Dimensional analysis questions frequently appear in exams. Practice verifying equations and deriving relationships using dimensions.