Dimensions and Derivation of Joule - Testbook.com

Unraveling the Dimensional Formula of Joule

The Joule, a unit of energy in the International System of Units (SI), has a specific dimensional formula, which is as follows:

[M¹L²T^-2]

Here's what each symbol in the formula represents:

• M stands for Mass
• L signifies Length
• T denotes Time

How to Derive the Dimensions of Joule?

The Joule is the standard SI unit for work or energy. Therefore, its dimensional formula is the same as that of work or energy.

The formula for work done (W) is given by Force (F) multiplied by Displacement (D). Let's denote this as equation (1).

Force is the product of Mass (M) and acceleration (a). Thus, the dimensions of force become M¹L¹T^-2, as shown in equation (2).

Displacement is a measure of distance, so its dimensions are [M⁰L¹T⁰], as per equation (3).

Substituting the dimensions of force and displacement from equations (2) and (3) into equation (1), we get the dimensions of work or energy (also known as Joule) as follows:

Work (Joule)= F × D = [M¹L¹T^-2] × [L¹] = [M¹L²T^-2].

Hence, the dimensional representation of Joule is [M¹L²T^-2].

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