Class 11 Physics Chapter 1 Notes : SI Units and Fundamental_Derived Units Notes

Complete Notes on SI Units and Fundamental/Derived Units

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

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

Q1. What is the SI unit of power, and derive its dimensional formula.

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
Q2. Differentiate between fundamental units and derived units with examples.

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).
Q3. What is the SI unit of pressure, and express it in terms of fundamental units.

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.

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