Exercise Solutions Available
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Quick Summary
Measurement is the foundation of all scientific investigation. Class 9 extends measurement concepts to SI units, significant figures, errors in measurement, and the use of instruments like Vernier calipers and screw gauges. This chapter carries 1-mark and 3-mark questions regularly in board exams.
Key Definitions
- SI System: International System of Units — the globally accepted standard for measurement.
- Fundamental Units: Units that are independent of all other units (metre, kilogram, second, ampere, kelvin, mole, candela).
- Derived Units: Units formed by combining fundamental units (e.g., m/s for velocity, kg·m/s² for force).
- Significant Figures: All reliably known digits plus one estimated digit in a measurement.
- Error: The difference between measured value and true value.
- Least Count: The smallest value that can be measured by an instrument.
- Vernier Caliper: Instrument used to measure lengths with 0.01 cm accuracy.
- Screw Gauge: Instrument used to measure very small lengths with 0.001 cm (0.01 mm) accuracy.
SI Fundamental Units Table
| Physical Quantity | SI Unit | Symbol |
|---|---|---|
| Length | Metre | m |
| Mass | Kilogram | kg |
| Time | Second | s |
| Electric Current | Ampere | A |
| Temperature | Kelvin | K |
| Amount of Substance | Mole | mol |
| Luminous Intensity | Candela | cd |
Significant Figures Rules
1. All non-zero digits are significant (e.g., 423 has 3 significant figures). 2. Zeros between non-zero digits are significant (e.g., 4023 has 4 significant figures). 3. Leading zeros are not significant (e.g., 0.0045 has 2 significant figures). 4. Trailing zeros after a decimal point are significant (e.g., 2.500 has 4 significant figures). 5. Trailing zeros in a whole number without a decimal may or may not be significant.
Types of Errors
Systematic Errors
- Errors that occur consistently due to faulty instruments or incorrect technique.
- Examples: zero error in Vernier caliper, parallax error, calibration error.
Random Errors
- Errors that vary unpredictably from measurement to measurement.
- Can be reduced by taking multiple readings and calculating the mean.
Gross Errors
- Errors caused by carelessness or mistakes by the observer.
- Example: misreading the scale.
Vernier Caliper
- Used to measure internal and external diameters, and depth.
- Least count = 1 MSD − 1 VSD = 0.01 cm
- Reading = Main scale reading + (Vernier scale coinciding division × Least count)
Screw Gauge
- Used to measure the diameter of thin wires and thickness of sheets.
- Least count = Pitch ÷ Number of divisions on circular scale = 0.01 mm
- Reading = Main scale reading + (Circular scale division × Least count)
Important Questions
One Mark
- State the SI unit of temperature.
- What is the least count of a screw gauge?
- Define significant figures.
- How many significant figures are there in 0.00420?
- What is the difference between systematic and random errors?
Short Answer (3 marks)
- Explain how to read a Vernier caliper with an example.
- State the rules for determining significant figures with three examples.
- Distinguish between fundamental and derived quantities with examples.
Long Answer (5 marks)
- Describe the construction and working of a screw gauge. How do you determine zero error?
- Explain the types of errors in measurement with examples and methods to minimise them.
Common Mistakes
- Confusing accuracy with precision — remember: accuracy = close to true value; precision = close to each other.
- Forgetting to count zeros between non-zero digits as significant.
- Not applying zero correction when reading Vernier caliper or screw gauge.
Revision Checklist
- [ ] Memorised all 7 SI fundamental units and their symbols
- [ ] Can apply significant figure rules to any number
- [ ] Know how to calculate least count for Vernier caliper and screw gauge
- [ ] Understand the three types of errors
- [ ] Practised 1-mark, 3-mark, and 5-mark question formats