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].
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