Dimensional Formula of Joule
The dimensional formula of Joule is given by,
[M1 L2 T-2]
- M = Mass
- L = Length
- T = Time
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].