In Units and Measurement, students explore the fundamental language of physics through the International System of Units (SI). This chapter builds a strong foundation by explaining the importance of measurement standards, unit conversions, and dimensional analysis. Students learn to differentiate between fundamental and derived units while developing essential skills in error analysis and significant figures that will serve them throughout their physics journey.
Chapter 2: Units and Measurement
Plus One Physics – SCERT Board
1. Introduction to Measurement
- Definition: Measurement is the process of comparing a physical quantity with a standard unit.
- Components: Every measurement consists of:
- A numerical value
- A unit
- Expression: Physical quantity = Numerical value × Unit
2. Need for Standard Units
- Allows uniform communication of measurements across the world
- Ensures reproducibility and reliability of scientific experiments
- Facilitates comparison of experimental results
- Necessary for accurate trade and commerce
3. Evolution of Measurement Systems
- Early systems: Based on human body parts (cubit, foot, span)
- CGS system: Centimeter, Gram, Second
- FPS system: Foot, Pound, Second
- MKS system: Meter, Kilogram, Second
- SI system: The modern International System of Units (Système International d’Unités)
4. The SI System
4.1 Base Units
| Physical Quantity | SI Unit | Symbol |
| Length | Meter | m |
| Mass | Kilogram | kg |
| Time | Second | s |
| Electric current | Ampere | A |
| Temperature | Kelvin | K |
| Amount of substance | Mole | mol |
| Luminous intensity | Candela | cd |
4.2 Definitions of Base Units
- Meter: Distance light travels in vacuum in 1/299,792,458 second
- Kilogram: Defined using Planck’s constant (h = 6.62607015 × 10^-34 kg·m²/s)
- Second: Duration of 9,192,631,770 periods of radiation from cesium-133 atom
- Ampere: Flow of 1/(1.602176634 × 10^-19) elementary charges per second
- Kelvin: Defined using the Boltzmann constant (k = 1.380649 × 10^-23 J/K)
- Mole: Amount containing exactly 6.02214076 × 10^23 elementary entities
- Candela: Luminous intensity in a given direction with frequency 540 × 10^12 Hz and radiant intensity of 1/683 watt per steradian
5. Derived Units
Units derived from the base units:
| Physical Quantity | SI Derived Unit | Symbol | Expression in Base Units |
| Force | Newton | N | kg·m/s² |
| Energy | Joule | J | kg·m²/s² |
| Power | Watt | W | kg·m²/s³ |
| Pressure | Pascal | Pa | kg/m·s² |
| Electric charge | Coulomb | C | A·s |
| Electric potential | Volt | V | kg·m²/s³·A |
| Resistance | Ohm | Ω | kg·m²/s³·A² |
| Frequency | Hertz | Hz | 1/s |
6. Prefixes for Units
For expressing very large or very small quantities:
| Prefix | Symbol | Multiplier | Power |
| Tera | T | 1,000,000,000,000 | 10^12 |
| Giga | G | 1,000,000,000 | 10^9 |
| Mega | M | 1,000,000 | 10^6 |
| Kilo | k | 1,000 | 10^3 |
| Hecto | h | 100 | 10^2 |
| Deca | da | 10 | 10^1 |
| – | – | 1 | 10^0 |
| Deci | d | 0.1 | 10^-1 |
| Centi | c | 0.01 | 10^-2 |
| Milli | m | 0.001 | 10^-3 |
| Micro | μ | 0.000001 | 10^-6 |
| Nano | n | 0.000000001 | 10^-9 |
| Pico | p | 0.000000000001 | 10^-12 |
7. Dimensional Analysis
- Dimensions: The physical nature of a quantity expressed in terms of base quantities
- Uses:
- Checking correctness of equations
- Deriving relationships between physical quantities
- Converting units from one system to another
7.1 Dimensional Formulas of Common Physical Quantities
| Physical Quantity | Dimensional Formula |
| Length | [L] |
| Mass | [M] |
| Time | [T] |
| Area | [L²] |
| Volume | [L³] |
| Velocity | [LT^-1] |
| Acceleration | [LT^-2] |
| Force | [MLT^-2] |
| Work/Energy | [ML²T^-2] |
| Power | [ML²T^-3] |
| Pressure | [ML^-1T^-2] |
| Density | [ML^-3] |
| Momentum | [MLT^-1] |
7.2 Principles of Dimensional Analysis
- Principle of Homogeneity: All terms in an equation must have the same dimensions
- Limitations:
- Cannot determine dimensionless constants
- Cannot distinguish between similar dimensional quantities (e.g., work and torque)
- Cannot verify equations with trigonometric, logarithmic, or exponential functions
8. Measurement of Length
- Direct methods: Using meter scale, vernier caliper, screw gauge, etc.
- Indirect methods: Using light waves, lasers, etc.
- Range of lengths: From subatomic particles (~10^-15 m) to the observable universe (~10^26 m)
9. Measurement of Mass
- Common instruments: Physical balance, electronic balance
- Range of masses: From electron mass (~10^-30 kg) to galaxy mass (~10^41 kg)
10. Measurement of Time
- Common devices: Atomic clocks, quartz clocks, pendulum clocks
- Range of time: From very short intervals (particle decay ~10^-23 s) to age of universe (~10^17 s)
11. Accuracy, Precision, and Errors in Measurement
- Accuracy: How close a measurement is to the true value
- Precision: The reproducibility of measurements
- Types of errors:
- Systematic errors: Due to instrument defects, calibration issues, or procedural flaws
- Random errors: Due to unpredictable fluctuations in experimental conditions
- Gross errors: Due to carelessness or human mistakes
12. Significant Figures
- Definition: Digits that carry meaningful information about a measurement
- Rules for counting significant figures:
- All non-zero digits are significant
- Zeros between non-zero digits are significant
- Leading zeros are not significant
- Trailing zeros in a number with a decimal point are significant
- Rules for arithmetic operations:
- Addition/Subtraction: Result has the same precision as the least precise measurement
- Multiplication/Division: Result has the same number of significant figures as the measurement with the fewest significant figures
13. Rounding Off
- Rules:
- If the digit to be dropped is less than 5, leave the preceding digit unchanged
- If the digit to be dropped is more than 5, increase the preceding digit by 1
- If the digit to be dropped is exactly 5, round to make the preceding digit even
14. Order of Magnitude
- Definition: The power of 10 nearest to the given number
- Estimation: Useful for quick calculations and verification
15. Summary
- Measurements are essential in physics and require standardized units
- The SI system provides a coherent set of units based on seven base units
- Dimensional analysis helps in checking equations and converting units
- Understanding significant figures, errors, and accuracy is crucial for reliable measurements
- The range of measurements in physics spans from subatomic particles to the universe itself.
Complete Chapter-wise Hsslive Plus One Physics Notes
Our Hsslive Plus One physics notes cover all chapters with key focus areas to help you organize your study effectively:
- 1. Physical World Notes
- 2. Units and Measurements Notes
- 3. Motion in a Straight Line Notes
- 4. Motion in a Plane Notes
- 5. Laws of Motion Notes
- 6. Work, Energy and Power Notes
- 7. System of Particles and Rotational Motion Notes
- 8. Gravitation Notes
- 9. Mechanical Properties of Solids Notes
- 10. Mechanical Properties of Fluids Notes
- 11. Thermal Properties of Matter Notes
- 12. Thermodynamics Notes
- 13. Kinetic Theory Notes
- 14. Oscillations Notes
- 15. Waves Notes