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The dimensional formula of power is-
1. MLT-2
2. ML2T-2
3. ML2T-3
4. ML-1T-2

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Correct Answer - Option 3 : ML2T-3

Concept:

Dimensional Formula

  • It depicts the way to relate any unit to fundamental Units.
  • If we have to find The dimensional formula of any quantity, At first, we find its units in terms of these fundamental units, and then replace units with these dimensions.

Power

  •  The rate of consumption of energy is called power.

P = Δ E / Δt

Δ E = Change in energy, Δt = Change in time

  • Unit of Power: The unit of power is Watt

1 watt = 1 Joule / 1 second

Calculation:

Dimension of Power

\(P = \frac{Dimension\ of \ Energy}{Dimension \ of \ time}\)

Dimension of Energy = Dimension of Work = Dimension of Force × Dimension of displacement 

E = [ M L T -2 ]  [ L ] = M L 2 T - 2 

⇒ P = E / T

\(\implies P = \frac{M L ^{2} T^{-2}}{T} = M L ^{2}T^{-2}T^{-1}\)

⇒ P = M L 2 T (-2 - 1 )  = M L 2 T -3

So, the correct option is ML2T-3

Additional Information:

  • Dimensional Formula of Fundamental Units are

 

Physical Quantity

SI Unit

Dimension

Mass

Kg

M

Time

Second


T

Length

Meter

L

Current

Ampere

I

Temperature

Kelvin

K

 

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