Units and Dimensions is a fundamental and essential topic in Physics. For the measurement of a physical quantity, Unit plays a vital role. Unit provides a complete idea about the measurement of a physical quantity. Dimension is a measure of the size or extent of a particular quantity.
Table of Contents
What are Units?
Units are values used to measure and express various physical quantities. Unit gives us a complete and clear idea about a physical quantity. Measurement of a physical quantity consists of mainly two parts – Numeric value and unit.
Measurement of physical quantity = Numerical value x Unit
For example, A rectangular garden has 50 meter length.
Here, “50” is the numeric value or magnitude, and “meter” is the Unit of the physical quantity.
Fundamental and Derived Units
- Fundamental Units are independent to each other and these units are mainly used to measure the units of the fundamental physical quantities. There are seven fundamental units available namely – meter, kilogram, second, ampere, kelvin, candela and mole.
- Derived Units are the units which are obtained from the fundamental units. Except fundamental units, all other units are known as Derived Units. The examples of Derived units are units of area, volume, momentum, speed, velocity, density, force, energy, work etc.
Fundamental Units
Fundamental units are also known as base units. There are total of 7 base units. Fundamental units and their Symbols in SI systemare discussed in the following table:
| Physical Quantity | Name of Unit | Symbol |
|---|---|---|
| Length | meter | m |
| Mass | kilogram | kg |
| Time | second | s |
| Electric current | ampere | A |
| Thermodynamic temperature | kelvin | K |
| Amount of substance | mole | mol |
| Luminous intensity | candela | cd |
System of Units
There are four system of units available namely – MKS System, CGS System, FPS System, and SI system.
MKS System: The full form ofMKS System is Metre Kilogram Second. In MKS system, the units of length, mass and time are respectively metre, kilogram and second.
CGS System : The full form of CGS system is Centimetre Gram Second. CGS system is also known as Gaussian system. In CGS system, the units of length, mass and time are respectively centimetre, gram and second.
FPS System : The full form of FPS System is Foot Pound Second. FPS is also known as British system. In FPS system, the units of length, mass and time are respectively foot, pound and second.
SI System : SI system is generally known as International System of Units. It is the modification form of MKS system. SI System of unit is adopted to have same common unit world-wide.
Macro and Micro Prefixes
Micro- is a prefix used to describe something that is small scale, while macro- is a prefix used to describe something that is large scale.
| Macro Prefix | Symbol | Value |
|---|---|---|
| kilo | k | 103 |
| mega | M | 106 |
| giga | G | 109 |
| tera | T | 1012 |
| peta | P | 1015 |
| exa | E | 1018 |
| zetta | Z | 1021 |
| yotta | Y | 1024 |
| Micro Prefix | Symbol | Value |
|---|---|---|
| centi | c | 10-2 |
| milli | m | 10-3 |
| micro | μ | 10-6 |
| nano | n | 10-9 |
| pico | p | 10-12 |
| femto | f | 10-15 |
| atto | a | 10-18 |
| zepto | z | 10-21 |
| yocto | y | 10-24 |
Units of Length, Mass and Time
The different units used to represent length, mass and time are shown below in the table:
| Units of Length | Units of Mass | Units of Time |
|---|---|---|
| 1 Angstrom = 10-10 m | 1 Quintal = 102 kg | 1 minute = 60 second |
| 1 Light year = 9.46 × 1015 m | 1 Metric tone = 103 kg | 1 Hour = 60 minute = 3600 second |
| 1 AU ( Astronomical Unit) = 1.5 × 1011 m | 1 Atomic mass unit = 1.66 × 10-27 kg | 1 Day = 24 hours = 1440 min = 86400 s |
| 1 Mile = 1.6 km | 1 Pound = 0.4537 kg | 1 Lunar month = 28 days |
| 1 Fermi = 10-15 m | 1 Slug = 14.59 kg | 1 Solar month = 30 or 31 days |
Important Formulas of Derived Units
Following table shows some of the examples of derived units from fundamental units.
What are Dimensions?
Dimensions of a physical quantity are defined as the powers to which the fundamental quantities should be raised to represent that physical quantity. Dimension of a physical quantity is not dependent on the magnitude or the numeric value of that physical quantity.
To represent dimensions of physical quantities, we use square bracket “[ ]” around the quantity.
Dimensional Formula
Dimensional formula is nothing but an expression that shows how the fundamental units and which of the fundamental units are required to represent the unit of physical quantity.
The process of writing of a dimensional formula of a physical quantity is by enclosing the symbols of the base quantities with appropriate power in square brackets.
Dimensions of fundamental physical quantities along with their dimensional symbols are written as –
- [M] for Mass
- [L] for Length
- [T] for Time
- [I] for Electric Current
- [θ] for Temperature
- [J] for Luminous intensity
- [N] for Amount of substance
Dimensional Formulas for Physical Quantities
Some of the examples of dimensional formulas are as follows:
| Physical Quantity with Formula | Dimensional Formula |
|---|---|
| Area = Length × Breadth | [L × L] = [L2] = [M0L2T0] |
| Volume = Length × Breadth × Height | [L × L × L] = [L3] = [M0L3T0] |
| Speed = Distance/Time | [L]/[T] = [LT-1] = [M0L1T-1] |
| Velocity = Displacement/Time | [L]/[T] = [LT-1] = [M0L1T-1] |
| Acceleration = Velocity/Time | [LT-1]/[T] = [LT-2] = [M0L1T-2] |
| Pressure = Force/Area = (Mass × Acceleration)/Area | [MLT-2]/[L2] = [ML-1T-2] |
| Force = Mass × Acceleration | [M] [LT-2] = [MLT-2] |
| Work = Force × Displacement | [MLT-2] [L] = [ML2T-2] |
| Kinetic Energy = 1/2 × Mass × (Speed)2 | [M] [LT-1]2 = [ML2T-2] |
| Potential Energy = Mass × Acceleration due to gravity × Height | [M] [LT-2] [L] = [ML2T-2] |
| Impulse = (force x time) | [MLT-1] |
Quantities Having the Same Dimensional Formula
The following physical quantities have the same Dimensional formula:
- Momentum and Impulse
- Work, torque, energy, the moment of force
- Planck’s constant, Angular momentum, rotational impulse
- Pressure, Stress, modulus of elasticity, energy density.
- Force constant, surface tension, surface energy.
- Frequency, Angular velocity, velocity gradient.
- Gravitational potential, latent heat.
- Entropy, Thermal capacity, universal gas constant and Boltzmann’s constant.
- Force, thrust.
- Power, luminous flux.
Dimensionless Quantities
Dimensionless quantities are the physical quantities which have no dimension or zero dimension. Its numeric value or magnitude is same in all system of units.
Examples : The examples of dimensionless quantities are as follows:
- Angle
- Solid angle
- Relative density
- Specific gravity
Uses of Dimension
Dimension of a physical quantity is an essential part. It has following uses –
- It is used to convert the units from one measurement system to another measurement system.
- It helps to establish relationship among various physical quantities.
- It is used to ensure an equation is homogeneous or not.
FAQs on Units and Dimensions
What are the 7 dimension units?
The seven dimension base units are as follows –
- Length – meter (m)
- Time – second (s)
- Amount of substance – mole (mole)
- Electric current – ampere (A)
- Temperature – kelvin (K)
- Luminous intensity – candela (cd)
- Mass – kilogram (kg)
What is the SI unit of speed?
The SI unit of speed is m/s or m s-1.
What is the SI unit of temperature?
The SI unit of temperature is kelvin.
What is the SI unit for energy?
The SI unit of energy is joule.
What are Dimensional Variables?
The physical quantities which have dimensions but do not have fixed numerical value, is called the Dimensional Variables. Examples : velocity, acceleration, force, work, power, etc are the examples of Dimensional variables.
What is Dimensional Analysis?
Dimensional analysis can be defined as the process of checking relations among various physical quantities by using the dimensions of the physical quantities. These are independent of the numerical values and constants.
What are Dimensional Constants?
The physical quantities those have dimensions and have fixed values, are called dimensional constants. For Example:
- Gravitational constant (G)
- Planck’s constant (h)
- Velocity of light in a vacuum (C)
- Universal gas constant (R)
What is Law of Homogeneity of Dimensions?
Principle of Homogeneity states that dimensions of each of the terms of a dimensional equation on both sides should be the same.
