Unit & Dimensions (By Er. Md Aslam)

Dear students,

My name is Er. Md Aslam, and I welcome you to our first and one of the most important chapters in physics: Unit and Dimensions. Physics is the language of nature. Every event in the natural world—whether it is the motion of planets, the vibration of a guitar string, the boiling of water, or the working of a mobile phone—is described using measurements. To understand nature clearly, we must measure physical quantities correctly and express them in standard forms.

This chapter is your entry gate into the world of scientific accuracy. Before solving big problems in mechanics, electricity, or modern physics, you must learn how to measure, how to express quantities, and how to check if your answers are correct. That is why Unit and Dimensions is placed at the very beginning of Class 11 Physics.

Understanding this chapter will make the rest of physics much easier.

Let us begin our journey with curiosity and clarity.

Short Notes: Unit & Dimensions (Class 11 Physics)

1. Physical Quantities

• Any quantity that can be measured is called a physical quantity.
  Examples: length, mass, time, velocity, force, energy, temperature.

2. Units

• A unit is a standard used to measure a physical quantity.
  Example: metre (m), kilogram (kg), second (s).

Types of Units

1. Fundamental (Base) Units – Cannot be derived from other units.
• SI base units: m, kg, s, A, K, mol, cd.
3. Derived Units – Obtained from base units.
• Example: speed = m/s, force = kg·m/s² (Newton).

3. Dimensions

• The dimensions of a physical quantity show how it depends on fundamental quantities.
• Represented as:
• Length → [L]
• Mass → [M]
• Time → [T]

Examples

• Velocity → [L T⁻¹]
• Acceleration → [L T⁻²]
• Force → [M L T⁻²]

4. Dimensional Formula

• Expression that shows the powers of fundamental dimensions.
  Example:
• Force = [M¹ L¹ T⁻²]

5. Uses of Dimensions

1. Check correctness of formulas (Dimensional Analysis)
2. Convert units (e.g., km/h to m/s)
3. Derive relationships between physical quantities
4. Identify new quantities from an equation

6. Significant Figures (Optional Part)

• Used to express accuracy of measurement.
  Example: 3.28 has 3 significant figures.

7. Errors in Measurement

• No measurement is 100% exact.
• Types of errors:
• Systematic errors
• Random errors
• Absolute, Relative, Percentage error