# Dimension Analysis in Physics For WAEC and UTME

In this article, I will help students understand how to get the dimensions of Pressure, Power, Force, Density, And Energy. Kindly note that before we proceed, we must first know the dimensions of the fundamental quantities that we have.

In Physics, dimensional analysis is the study of the relation between physical quantities based on their units and dimensions. It is used to convert a unit from one form to another. Also, it will be easy to know the S.I base unit of any quantity in physics.

Any quantity which can be measured in units of length is said to have a dimension, of length (L). So also any quantity which can be measured in units of time is said to have a dimension of Time (T) and any quantity which can be measured in units of mass is said to have a dimension of Mass (Mass).

In physics, the word dimension has a special meaning. It usually denotes the physical nature of quantity. The symbols that are used to specify length, mass, and time are [L], [M], [T], respectively. They are usually enclosed in brackets.

Physical Quantity | Dimension |

Length | [L] |

Mass | [M] |

Time | [T] |

For example, the dimension of volume is [L^{3 }]. Volume is length x length x length = L X L X L = L^{3}

Read: Dimension of impulse and momentum

**Pressure**

Pressure is defined as force per area. This can be represented mathematically as P = F/A

Force = Mass X acceleration = Mass x Velocity/Time = Mass x distance/T^{2} = M x L X T^{-2} = [MLT^{-2}]

Area = Length x Length =[ L^{2}]

Therefore, the dimension of pressure is = [MLT^{-2}]/ L^{2} = [ ML^{-1}T^{-2}]

**Power**

Power is defined as the rate of energy expended. This can be represented mathematically as Power = Force x Velocity

Force = Mass X acceleration = Mass x Velocity/Time = Mass x distance/T^{2} = M x L X T^{-2} = [MLT^{-2}]

Velocity = displacement/ Time = L/T = [ LT^{-1}]

Therefore, the dimension of power is [MLT^{-2}] /[ LT^{-1}] = [ML^{2}T^{-3}]

**Force**

Force is the product of mass and acceleration. Force = Mass X acceleration = Mass x Velocity/Time = Mass x distance/T^{2} = M x L X T^{-2} = [MLT^{-2}]

Therefore, the dimension of force is [MLT^{-2}]

**Density**

Density is mass divided by volume i.e. Mass/Volume = M/L^{3} = ML^{-3}

The dimension of density = [ML^{-3} ]

**Energy**

Energy is the ability to do work. Mathematically, energy = Force x distance

Force = [MLT^{-2}]

Distance = [L]

Dimension of energy = [MLT^{-2}] / [L] = [MT^{-2}]