1. Unit and Dimension

📘 Unit and Dimension: Summary Note for MCQ

 “Unit and Dimension” lesson includes a Quick summary note for NEB Bridge Course students.

Unit and Dimension

🔹 1. Physical Quantities

  • Fundamental Quantities: Basic quantities that cannot be derived from others.
    Examples: Length (L), Mass (M), Time (T), Current (A), Temperature (K), Luminous Intensity (cd), Amount of Substance (mol)

  • Derived Quantities: Quantities derived from fundamental ones.
    Examples: Speed, Force, Work, Pressure

🔹 2. Units

  • Unit: Standard of measurement of a physical quantity.

⚖️ Types of Units:

  • Fundamental Units: Units of fundamental quantities (e.g., meter, kilogram, second)

  • Derived Units: Units derived from fundamental units (e.g., m/s, N, J)

🌍 System of Units:

SystemLengthMassTime
CGScmgs
MKSmkgs
SImkgs

🔹 3. Dimensions

  • Dimensions: The powers to which fundamental quantities are raised to represent a physical quantity.

✅ Dimension of Physical Quantities:

Examples:

  • Velocity: [M⁰L¹T⁻¹]

  • Acceleration: [M⁰L¹T⁻²]

  • Force: [MLT⁻²]

  • Work: [ML²T⁻²]

  • Pressure: [ML⁻¹T⁻²]

🔹 4. Dimensional Formula

  • Expresses a physical quantity in terms of basic dimensions: M (mass), L (length), T (time), etc.

Example:
Work = Force × Distance
→ [Work] = [MLT⁻²] × [L] = [ML²T⁻²]

🔹 5. Applications of Dimensional Analysis

  1. To check the correctness of the formula (Principle of Homogeneity)

    • All terms must have the same dimensions.

  2. To derive a relation between physical quantities

  3. To convert units from one system to another

⚠️ Limitations of Dimensional Analysis

  • Cannot detect dimensionless constants (like sin, cos, tan)

  • Cannot verify if a formula has addition/subtraction of unlike quantities

  • Cannot derive equations involving more than one term added/subtracted

🧠 Important Dimensionless Quantities

  • Angle (radian)

  • Strain

  • Refractive index

  • Specific gravity

  • Poisson’s ratio

All have dimension = 1 (i.e., dimensionless)

🔢 Key MCQ Points

  • SI unit of Force = Newton (N) = kg·m/s²

  • SI unit of Pressure = Pascal (Pa) = N/m²

  • Dimensions of Energy = [ML²T⁻²]

  • Power = [ML²T⁻³]

  • Dimensional formula of Planck’s constant = [ML²T⁻¹]

  • Dimensional formula of Universal Gravitational Constant (G) = [M⁻¹L³T⁻²]

🏁 Quick Tricks

  • If you forget the dimension, break it into known formulas.

    • e.g. Pressure = Force/Area → [MLT⁻²]/[L²] = [ML⁻¹T⁻²]

  • Use dimensional analysis to eliminate the wrong MCQ options.

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