# Dimensions of Intensity

## Dimensional Formula of Intensity

The dimensional formula of Intensity is given by,

[M1 L0 T-3]

Where,

• M = Mass
• L = Length
• T = Time

### Derivation

Intensity (I) = Power × [Area]-1 . . . . . (1)

The dimensional formula of area = [M0 L2 T0] . . . . (2)

Since, Power = Work × [Time]-1 . . . . (3)

And, Work = Force × Displacement = M × a × Displacement

⇒ Work = [M] × [M0 L1 T-2] × [L]

Therefore, the dimensional formula of work = [M1 L2 T-2] . . . . (4)

On substituting equation (4) in equation (3) we get,

Power = [M1 L2 T-2] × [M0 L0 T1]-1

Therefore, the dimensional formula of power = [M1 L2 T-3] . . . . (5)

On substituting equation (2) and (5) in equation (1) we get,

Intensity (I) = Power × [Area]-1

Or, I = [M1 L2 T-3] × [M0 L2 T0]-1 = [M1 L0 T-3]

Therefore, the time period is dimensionally represented as [M1 L0 T-3].