Complete Notes on SI Units and Fundamental/Derived Units
Why SI Units are Important
The SI system provides a standardized framework for measurements, essential for solving physics problems and answering theoretical questions in CBSE, NEET, and JEE exams. Understanding fundamental and derived units is key to mastering numerical and conceptual questions.
1. Definition
The SI system is an international standard for measurements, using fundamental units for base quantities and derived units for quantities expressed as combinations of these.
2. Key Units and Dimensions
Below are the fundamental units and selected derived units with their formulas, SI units, and dimensional formulae:
- Fundamental Units:
- Mass: Kilogram (kg), [M]
- Length: Meter (m), [L]
- Time: Second (s), [T]
- Electric Current: Ampere (A), [I]
- Temperature: Kelvin (K), [θ]
- Amount of Substance: Mole (mol), [N]
- Luminous Intensity: Candela (cd), [J]
- Derived Units:
- Force: F = ma
- SI Unit: Newton (N = kg·m/s²)
- Dimensional Formula: [M][L][T]-2
- Work/Energy: W = F·d
- SI Unit: Joule (J = N·m)
- Dimensional Formula: [M][L]2[T]-2
- Power: P = W/t
- SI Unit: Watt (W = J/s)
- Dimensional Formula: [M][L]2[T]-3
- Pressure: P = F/A
- SI Unit: Pascal (Pa = N/m²)
- Dimensional Formula: [M][L]-1[T]-2
- Velocity: v = d/t
- SI Unit: Meter per second (m/s)
- Dimensional Formula: [L][T]-1
- Force: F = ma
3. Real-Life Example
- Electrical Appliances: The power rating of a bulb is given in watts (W), a derived SI unit. For example, a 60 W bulb indicates energy consumption per second, helping consumers calculate electricity costs.
4. Common Exam Questions and Answers
Answer:
- SI Unit: Watt (W)
- Derivation: Power = Work / Time
- Work = Force × Distance = [M][L][T]-2 × [L] = [M][L]2[T]-2
- Power = [M][L]2[T]-2 / [T] = [M][L]2[T]-3
Answer:
- Fundamental Units: Base units for fundamental quantities, e.g., meter (m) for length ([L]), kilogram (kg) for mass ([M]).
- Derived Units: Combinations of fundamental units, e.g., Newton (N = kg·m/s²) for force ([M][L][T]-2), Pascal (Pa = N/m²) for pressure ([M][L]-1[T]-2).
Answer:
- SI Unit: Pascal (Pa)
- Pressure = Force / Area = (kg·m/s²) / m² = kg·m-1·s-2
- In fundamental units: kg·m-1·s-2
5. Diagram/Table
The table below lists fundamental and derived units with their SI units and dimensions, serving as a visual reference:
Quantity | Type | SI Unit | Dimensional Formula |
---|---|---|---|
Mass | Fundamental | Kilogram (kg) | [M] |
Length | Fundamental | Meter (m) | [L] |
Time | Fundamental | Second (s) | [T] |
Force | Derived | Newton (N) | [M][L][T]-2 |
Energy | Derived | Joule (J) | [M][L]2[T]-2 |
Power | Derived | Watt (W) | [M][L]2[T]-3 |
Pressure | Derived | Pascal (Pa) | [M][L]-1[T]-2 |
6. Quick Tips/Tricks
- Fundamental Units: Memorize the 7 base units: kg, m, s, A, K, mol, cd.
- Derived Units: Break down derived units into fundamental ones (e.g., Newton = kg·m/s²).
- NEET/JEE Trick: Use dimensional analysis to verify units in calculations (e.g., Power = [M][L]2[T]-3 = W).
- Memorization: Link units to quantities: “Newton for force, Joule for energy, Watt for power, Pascal for pressure.”
- Quick Check: Ensure units match on both sides of an equation to confirm correctness.
Note: Mastering SI units and their dimensions is essential for solving numerical problems and understanding physical quantities in physics.