Dimensional Formula of Joule

The dimensional formula of Joule is given by,

[M¹ L² T^-2]

Where,

• M = Mass
• L = Length
• T = Time

Derivation

Joule is the SI unit of work done. Therefore, the dimensional formula of Joule is the same as that of the work done.

Since, Work done (W) = Force × Displacement . . . . (1)

And, Force = Mass × acceleration = M¹ × [M⁰ L T^-2]

∴ The dimensions of force = M¹ L¹ T^-2 . . . . (2)

Also, the dimensions of displacement = [M⁰ L¹ T⁰] . . . . (3)

On substituting equation (2) and (3) in equation (1) we get,

Work (Joule)= F × D = [M¹ L¹ T^-2] × [L¹] = [M¹ L² T^-2].

Therefore, Joule is dimensionally represented as [M¹ L² T^-2].

⇒ Check Other Dimensional Formulas:

• Dimensions of Electric Field
• Dimensions of Reynolds Number
• Dimensions of Newton
• Dimensions of Rotational Kinetic Energy
• Dimensions of Gravitational Potential Energy