Echoes Within

📘 Unit and Dimension: Summary Note for MCQ

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

🔹 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:

🔹 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.

You Can Also Read:

• Use of Fundamental Units in Physical Equations to Examine Their Homogeneity
•  full text documents, including the curriculum, CDC eLibrary