Units and Dimensions
SI base and derived units and dimensional formulae of physical quantities. (Physics › Physical World, Units and Measurements, NEET UG syllabus.)
What is Units and Dimensions?
A universally accepted standard of measurement for a physical quantity.
Key formula / rule: Velocity
Key points
- Identify the 7 SI base units and their symbols.
- Distinguish between base and derived units.
- Determine the dimensional formula for various physical quantities.
- Apply the principle of homogeneity to check the dimensional consistency of equations.
Common exam trap
Confusing units with dimensions.
Definitions
- Term
Unit
- Meaning
A universally accepted standard of measurement for a physical quantity.
- Term
Dimension
- Meaning
The powers to which the fundamental units must be raised to represent a physical quantity.
- Term
Dimensional Formula
- Meaning
An expression showing how and which of the base quantities are included in a physical quantity, represented by symbols like [M], [L], [T].
- Term
Dimensional Analysis
- Meaning
A method based on the principle of homogeneity used to check the consistency of equations, derive relations, and convert units.
- Term
Principle of Homogeneity
- Meaning
States that the dimensions of all the terms on both sides of a physical equation must be identical.
Learning objectives
Identify the 7 SI base units and their symbols.
Distinguish between base and derived units.
Determine the dimensional formula for various physical quantities.
Apply the principle of homogeneity to check the dimensional consistency of equations.
Use dimensional analysis to derive relationships between physical quantities.
Understand the limitations of dimensional analysis.
Convert units between different systems using dimensional analysis.
Formulae
- Name
Velocity
- Note
Distance/Time
- Expression
[L][T]⁻¹
- Name
Acceleration
- Note
Velocity/Time
- Expression
[L][T]⁻²
- Name
Force
- Note
Mass × Acceleration
- Expression
[M][L][T]⁻²
- Name
Work/Energy/Torque
- Note
Force × Distance
- Expression
[M][L]²[T]⁻²
- Name
Power
- Note
Work/Time
- Expression
[M][L]²[T]⁻³
- Name
Pressure/Stress
- Note
Force/Area
- Expression
[M][L]⁻¹[T]⁻²
- Name
Momentum
- Note
Mass × Velocity
- Expression
[M][L][T]⁻¹
- Name
Frequency
- Note
1/Time Period
- Expression
[T]⁻¹
- Name
Gravitational Constant (G)
- Note
From F = Gm₁m₂/r²
- Expression
[M]⁻¹[L]³[T]⁻²
- Name
Planck's Constant (h)
- Note
From E = hν
- Expression
[M][L]²[T]⁻¹
Prerequisites
Basic understanding of physical quantities (mass, length, time, force, energy, etc.).
Basic algebraic manipulation of exponents.
Common mistakes
Confusing units with dimensions.
Incorrectly identifying base units for derived quantities (e.g., thinking Newton is a base unit).
Errors in algebraic manipulation of powers when deriving dimensional formulae.
Forgetting that dimensionless constants cannot be determined by dimensional analysis.
Applying dimensional analysis to equations with trigonometric or exponential terms directly without considering their arguments must be dimensionless.
Not knowing the dimensional formulae of common physical constants.
Keywords
Units
Dimensions
SI Units
Base Units
Derived Units
Dimensional Formula
Dimensional Analysis
Homogeneity
Physical Quantity
Measurement
Practice preview
Which of the following is an SI base unit?…
easy
The dimensional formula for speed is:…
easy
Which pair of physical quantities has the same dimensions?…
medium