Dimension of a physical quantity.

By Santosh Chaudhary, M.Sc (Physics)

Nalanda Open University 

What is Dimension ?

Dimension of physical quantities is a way of expressing the dependence of a physical quantity on the fundamental units of mass, length, time, temperature, electric current, luminous intensity, and amount of substance.

The dimension of a physical quantity is the way it is expressed in terms of the fundamental quantities. The fundamental quantities are the basic units of measurement that cannot be further reduced. In the SI system of units, there are seven fundamental quantities:

* Mass (M)

* Length (L)

* Time (T)

* Electric current (I)

* Temperature (Θ)

* Amount of substance (N)

* Luminous intensity (J)

All other physical quantities can be expressed in terms of these fundamental quantities. 

A general derived physical quantity can be expressed in the dimension formula as

Q=MᵃLᵇTᶜIᵈKᵉNᶠJᵍ

Where a,b,c,.. are the power of dependency.

For example, the dimension of force (F) is MLT⁻². This means that force is equal to mass multiplied by length divided by time squared.

The dimensions of physical quantities can be used to check the validity of equations. For example, if both sides of an equation do not have the same dimensions, then the equation is not valid.

Here are some examples of the dimensions of common physical quantities:

* Velocity: LT⁻¹

* Acceleration: LT⁻²

* Momentum: MLT⁻¹

* Energy: ML²T⁻²

* Power: ML²T⁻³

* Pressure: ML⁻¹T⁻²

* Volume: L³

* Density: ML⁻³

* Frequency: T⁻¹

The dimensions of physical quantities can be a useful tool for understanding the relationships between different quantities. They can also be used to check the validity of equations and to design experiments.