Exercise Solutions Available
Step-by-step answers for all textbook questions in this chapter
Quick Summary
This chapter introduces the scope of physics, physical quantities and their measurement, the SI system of units, dimensional analysis, and error analysis. It is foundational for all of Plus One and Plus Two Physics and forms a small but important part of NEET and JEE.
Key Concepts
- Physical quantity: Any quantity that can be measured (length, mass, time, etc.)
- Fundamental quantities: Cannot be derived from others (mass, length, time, temperature, current, luminous intensity, amount of substance)
- Derived quantities: Expressed in terms of fundamental quantities (velocity, force, energy)
- Unit: Standard reference quantity used for measurement
- SI system: International System of Units — the globally accepted measurement system
Fundamental and Derived Quantities
The Seven SI Base Units
| 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 |
Common Derived Units
| Quantity | Formula | SI Unit |
|---|---|---|
| Velocity | length / time | m s⁻¹ |
| Acceleration | velocity / time | m s⁻² |
| Force | mass × acceleration | kg m s⁻² = N |
| Energy / Work | force × distance | kg m² s⁻² = J |
| Pressure | force / area | kg m⁻¹ s⁻² = Pa |
| Power | work / time | kg m² s⁻³ = W |
Dimensional Analysis
Writing Dimensions
Dimensions of a quantity are expressed using symbols: M (mass), L (length), T (time), A (current), K (temperature).
| Quantity | Dimensional Formula |
|---|---|
| Velocity | [M⁰ L¹ T⁻¹] |
| Force | [M¹ L¹ T⁻²] |
| Energy | [M¹ L² T⁻²] |
| Pressure | [M¹ L⁻¹ T⁻²] |
| Power | [M¹ L² T⁻³] |
| Momentum | [M¹ L¹ T⁻¹] |
Uses of Dimensional Analysis
1. Checking correctness — Both sides of an equation must have the same dimensions 2. Deriving equations — Predict the form of a physical relationship 3. Unit conversion — Convert quantities between measurement systems
Limitations
- Cannot determine dimensionless constants
- Cannot check equations involving more than one term of the same dimension
- Cannot be used when a physical quantity depends on more than three fundamental quantities simultaneously
Error Analysis
Types of Errors
- Systematic errors: Consistent errors in one direction (instrument error, personal error, environmental error)
- Random errors: Irregular fluctuations in readings; reduced by taking multiple readings
- Gross errors: Large blunders due to carelessness — eliminated by careful observation
Absolute and Relative Error
- Absolute error = |True value − Measured value|
- Mean absolute error = Sum of all absolute errors / Number of readings
- Relative error = Mean absolute error / Mean value
- Percentage error = Relative error × 100
Error Propagation
For Z = A + B or Z = A − B: ΔZ = ΔA + ΔB
For Z = A × B or Z = A / B: ΔZ/Z = ΔA/A + ΔB/B
For Z = Aⁿ: ΔZ/Z = n × ΔA/A
Significant Figures
Rules: 1. All non-zero digits are significant 2. Zeros between non-zero digits are significant (e.g., 5004 has 4 significant figures) 3. Leading zeros are NOT significant (0.004 has 1 significant figure) 4. Trailing zeros in a decimal number ARE significant (3.50 has 3 significant figures)
Rounding: Drop digits beyond the desired precision; if the dropped digit is ≥ 5, round up.
Important Questions
One Mark
- What is a fundamental quantity? Give two examples.
- State the SI unit of luminous intensity.
- Define least count.
- What is the dimensional formula of pressure?
- What are systematic errors?
Short Answer (3 marks)
- Explain the uses of dimensional analysis with one example each.
- What are the types of errors in measurement? Define each type.
- Explain the rules for counting significant figures.
Long Answer (5 marks)
- Derive the dimensional formula for (a) velocity, (b) force, (c) work, (d) power, (e) pressure. State the SI unit for each.
- Explain error analysis. Define absolute error, mean absolute error, relative error, and percentage error. Give the rules for error propagation in addition and multiplication.
Common Mistakes
- Writing dimensions of derived quantities wrong — always build from the definition formula.
- Confusing accuracy (closeness to true value) with precision (closeness of repeated readings).
- Missing the factor of 100 when converting relative error to percentage error.
Board Exam Tips
- Memorise all 7 SI base units and their symbols.
- Practise 5–6 dimensional formula derivations — they appear frequently as short answers.
- Error analysis problems (numerical) appear in 3-mark and 5-mark sections.
- Remember: dimensionless quantities have dimensional formula [M⁰ L⁰ T⁰].
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