# The dimensional formula of power is-

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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

• 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