Physics ki bunyadi understanding ke liye fundamental quantities ka accurate measurement zaruri hai. Length, mass, aur time teen fundamental quantities hain jo all physical measurements ka base banati hain. Inka proper measurement scientific experiments, engineering, industry, aur daily life applications me bohot important hai.
1. Introduction
Measurement:
Process of determining the magnitude of a physical quantity compared to a standard unit.
- Without measurement, scientific analysis, calculations, and engineering design impossible hai.
- Measurement ke liye hamesha standardized units aur accurate instruments ka use hota hai.
Fundamental quantities: Length, Mass, Time
Derived quantities: Area, Volume, Density, Velocity, Acceleration, Force, etc., jo fundamental quantities se calculate hoti hain.
2. Measurement of Length
2.1 Definition
Length: Distance between two points in space.
2.2 Units of Length
- SI unit: meter (m)
- Historical definition: Originally defined using platinum-iridium bar
- Modern definition:
1 meter=distance light travels in vacuum in 1299,792,458 seconds1 \text{ meter} = \text{distance light travels in vacuum in } \frac{1}{299,792,458} \text{ seconds}1 meter=distance light travels in vacuum in 299,792,4581 seconds
2.3 Instruments for Measuring Length
| Instrument | Range / Accuracy | Use |
|---|---|---|
| Ruler / Scale | mm – m | Small objects |
| Vernier Caliper | 0.02 mm | Small length measurements |
| Micrometer Screw Gauge | 0.01 mm | High precision measurements |
| Screw Gauge / Micrometer | 0.001 cm | Very precise measurements |
| Measuring Tape | meters – tens of meters | Long distances |
| Optical Methods (Interferometer) | nm | Very fine measurements (physics labs) |
2.4 Vernier Caliper – Principle & Procedure
- Principle: Vernier scale gives fraction of main scale division
- Procedure:
- Clean object and jaws
- Place object between jaws
- Read main scale (MS)
- Read vernier scale (VS)
- Total length = MS + VS
- Least count (LC) = value of one main scale division – one vernier scale division
LC=1 MSD−1 VSDLC = 1 \text{ MSD} – 1 \text{ VSD}LC=1 MSD−1 VSD
- Example: MS = 2.0 cm, VS = 0.02 cm → Total = 2.02 cm
2.5 Micrometer Screw Gauge
- Measures very small lengths
- Principle: Screw moves object by small known distance per rotation
- Formula:
L=Main Scale Reading+Circular Scale Reading×LCL = \text{Main Scale Reading} + \text{Circular Scale Reading} \times LCL=Main Scale Reading+Circular Scale Reading×LC
- Least count typically: 0.01 mm
- Applications: Wire diameter, thickness of thin sheets
2.6 Errors in Length Measurement
- Systematic errors: Instrumental, environmental, personal
- Random errors: Fluctuations during measurement
- Parallax errors: Misalignment of eye and scale
- Methods to reduce errors: Multiple readings, proper calibration, careful observation
2.7 Applications of Length Measurement
- Engineering design
- Construction
- Manufacturing precision components
- Scientific experiments (optics, interferometry)
3. Measurement of Mass
3.1 Definition
Mass: Amount of matter contained in a body.
3.2 Units of Mass
- SI unit: kilogram (kg)
- Historical standard: Platinum-iridium cylinder kept at BIPM, Paris
- Modern definition: Based on Planck constant using Kibble balance
3.3 Instruments for Measuring Mass
| Instrument | Range / Accuracy | Use |
|---|---|---|
| Beam Balance | 1 mg – 10 kg | Laboratory measurements |
| Electronic Balance | 0.001 g – 100 kg | Quick and accurate measurements |
| Spring Balance | Up to 100 N | Weight measurement (force measurement) |
| Mass Comparator | µg – g | Very precise laboratory measurements |
3.4 Beam Balance – Principle & Procedure
- Principle: Equilibrium of torques
- Procedure:
- Place standard mass on one pan
- Place unknown mass on other pan
- Adjust until pointer at zero
- Record mass
- Errors:
- Friction at pivots
- Unequal arms
- Air currents
- Applications: Mass determination in physics, chemistry labs
3.5 Electronic Balance
- Based on electromagnetic force compensation
- Advantages: Fast, accurate, minimal human error
- Applications: Pharmaceutical, chemical, and industrial measurement
3.6 Relationship Between Mass and Weight
- Weight W=mgW = m gW=mg
- g = acceleration due to gravity
- Mass is constant, weight varies with location
3.7 Errors in Mass Measurement
- Zero error
- Sensitivity error
- Temperature effect
- Environmental vibrations
- Minimization: Proper calibration, controlled environment
4. Measurement of Time
4.1 Definition
Time: Duration between two events. Fundamental quantity in physics.
4.2 Units of Time
- SI unit: second (s)
- Historical: Fraction of solar day
- Modern definition (1967):
1 s=9,192,631,770 periods of radiation of Cs-133 atom1 \text{ s} = 9,192,631,770 \text{ periods of radiation of Cs-133 atom}1 s=9,192,631,770 periods of radiation of Cs-133 atom
4.3 Instruments for Measuring Time
| Instrument | Range / Accuracy | Use |
|---|---|---|
| Sand Clock / Hourglass | Minutes – hours | Historical |
| Mechanical Clock | Seconds – hours | Everyday timekeeping |
| Pendulum Clock | Seconds – hours | Historical laboratory use |
| Quartz Clock | Milliseconds – hours | Modern precise timing |
| Atomic Clock | 10⁻¹⁵ s | High precision physics experiments |
4.4 Pendulum Clock – Principle & Formula
- Principle: Time period of simple harmonic motion
T=2πlgT = 2\pi \sqrt{\frac{l}{g}}T=2πgl
Where:
- TTT = time period
- lll = length of pendulum
- ggg = acceleration due to gravity
- Used for measuring seconds accurately in labs
4.5 Quartz Oscillator
- Piezoelectric crystal vibrates at fixed frequency
- Frequency count → precise time measurement
- Applications: watches, clocks, computers
4.6 Atomic Clock
- Measures oscillations of atoms (Cesium-133)
- Accuracy: ±1 second in millions of years
- Basis for SI second definition
- Applications: GPS, satellite systems, scientific experiments
4.7 Errors in Time Measurement
- Human reaction delay
- Environmental influence on mechanical clocks
- Instrument calibration errors
- Minimized using atomic clocks and electronic timekeeping
5. Importance of Accurate Measurement
- Scientific experiments: Errors propagate in calculations
- Engineering: Precision required for machinery, construction
- Industry: Quality control depends on precise measurement
- Astronomy: Distance, mass, and time measurements critical
- Daily life: Timekeeping, weighing, construction, manufacturing
6. Units and Standards – SI System
- Length: meter (m)
- Mass: kilogram (kg)
- Time: second (s)
- Base units are universal and reproducible
- Derived units: m/s (velocity), N (force), kg/m³ (density), etc.
Importance:
- Universal comparison
- Scientific consistency
- Industrial standardization
7. Errors and Uncertainty
7.1 Types of Errors
- Systematic Error: Instrumental, environmental, calibration
- Random Error: Human reading variations
- Gross Error: Mistakes in observation
7.2 Expressing Measurement
- Absolute error:
Δx=∣xmeasured−xtrue∣\Delta x = |x_{measured} – x_{true}|Δx=∣xmeasured−xtrue∣
- Relative error:
δ=Δxxtrue×100%\delta = \frac{\Delta x}{x_{true}} \times 100\%δ=xtrueΔx×100%
- Significant figures: Indicate accuracy of measurement
8. Practical Examples
Example 1: Vernier Caliper Measurement
- Reading: MS = 3.0 cm, VS = 0.04 cm → Total = 3.04 cm
Example 2: Mass Determination
- Beam balance: unknown mass balances with 200 g + 50 g + 5 g → Mass = 255 g
Example 3: Time Measurement
- Quartz clock measures interval = 25.672 s
- Atomic clock confirms interval = 25.6719 s → Accuracy check
9. Summary Table
| Quantity | SI Unit | Instrument | Accuracy |
|---|---|---|---|
| Length | meter | Vernier, Micrometer | 0.01 – 0.001 mm |
| Mass | kilogram | Beam/Electronic Balance | 1 mg – µg |
| Time | second | Quartz/Atomic Clock | 10⁻¹⁵ s |
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