What is the Dimensional Formula of Power and its Derivation?

Dimensional Formula of Power

The dimensional formula of power is given by,

[M¹ L² T^-3]

Where,

• M = Mass
• L = Length
• T = Time

Derivation

Power (P) = Work × time^-1 = Joule × second^-1 . . . . . (1)

Since, Work (J) = Force (M x a) × displacement = M¹ L¹ T^-2 × [L]

Therefore, the dimensional formula of work = M¹ L² T^-2 . . . . (2)

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

Power (P) = Work × time^-1

Or, P = [M¹ L² T^-2] × [T^-1] = M¹ L² T^-3.

Therefore, power is dimensionally represented as M¹ L² T^-3.