Physical Quantities and Their Dimensional Formula
What is a Physical Quantity?
A physical quantity is any measurable property of a body, substance or phenomenon that can be expressed using a numerical value and a unit.
Examples
- Length
- Mass
- Time
- Force
- Energy
- Temperature
Types of Physical Quantities
Physical quantities are classified into three major categories:
- Fundamental Physical Quantities
- Derived Physical Quantities
- Supplementary Physical Quantities
Fundamental Physical Quantities
Fundamental quantities are independent quantities that cannot be expressed in terms of other physical quantities.
| Quantity | SI Unit | Dimension |
|---|---|---|
| Length | metre (m) | [L] |
| Mass | kilogram (kg) | [M] |
| Time | second (s) | [T] |
| Temperature | kelvin (K) | [Î] |
| Electric Current | ampere (A) | [I] |
| Amount of Substance | mole (mol) | [N] |
| Luminous Intensity | candela (cd) | [J] |
Derived Physical Quantities
Derived quantities are obtained by combining fundamental quantities through mathematical operations.
| Quantity | SI Unit | Dimensional Formula |
|---|---|---|
| Velocity | m/s | [LT⁻¹] |
| Acceleration | m/s² | [LT⁻²] |
| Force | Newton (N) | [MLT⁻²] |
| Energy | Joule (J) | [ML²T⁻²] |
| Power | Watt (W) | [ML²T⁻³] |
| Pressure | Pascal (Pa) | [ML⁻¹T⁻²] |
| Density | kg/m³ | [ML⁻³] |
| Area | m² | [L²] |
| Volume | m³ | [L³] |
Supplementary Physical Quantities
Supplementary quantities possess units but have no dimensions.
| Quantity | SI Unit | Symbol |
|---|---|---|
| Plane Angle | Radian | rad |
| Solid Angle | Steradian | sr |
What is Dimensional Formula?
A dimensional formula represents a physical quantity in terms of fundamental dimensions such as mass, length and time.
It indicates how a quantity depends on the fundamental quantities.
Examples of Dimensional Formula
| Physical Quantity | Dimensional Formula |
|---|---|
| Momentum | [MLT⁻¹] |
| Work | [ML²T⁻²] |
| Frequency | [T⁻¹] |
| Gravitational Constant | [M⁻¹L³T⁻²] |
| Surface Tension | [MT⁻²] |
Importance of Dimensional Analysis
- Checks correctness of equations.
- Converts units between systems.
- Derives relationships among quantities.
- Helps identify unknown formulas.
- Useful in physics and engineering calculations.
Frequently Asked Questions
What is a physical quantity?
A measurable property expressed using a numerical value and unit.
How many fundamental physical quantities are there?
Seven fundamental quantities in the SI system.
What is dimensional formula?
A representation of a physical quantity using fundamental dimensions.
What is the dimensional formula of force?
[MLT⁻²]
What is the dimensional formula of energy?
[ML²T⁻²]