Study Guides/Physics/Dimensional Formula of Power
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Dimensional Formula of Power

Power is defined as the rate at which work is done or energy is transferred. It tells us how fast a machine or person can do work.

Question (Click to Flip)

What is the dimension of power?

Answer

The dimensional formula of power is [M L² T⁻³].

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Key Facts

Formula: Power = Work / Time.

Dimensional Formula: [M L² T⁻³].

SI Unit: Watt (W).

1 Horsepower = 746 Watts.

Derivation

Step 1: The formula for Power is: Power = Work / Time

Step 2: Write the dimensions of Work and Time:

  • Dimension of Work = Force Ɨ Displacement = [M L² T⁻²]
  • Dimension of Time = [T]

Step 3: Substitute them into the formula: Power = [M L² T⁻²] / [T] Power = [M L² T⁻² · T⁻¹]

Final Dimensional Formula: [M L² T⁻³]

SI Unit

  • SI Unit: Watt (W) or Joules per second (J/s).
  • Commercial Unit: Horsepower (1 HP = 746 Watts).

Questions and Answers

What is the dimension of power?+

The dimensional formula of power is [M L² T⁻³].

How is the dimension of power derived?+

Power is Work divided by Time. Work is [M L² T⁻²] and Time is [T]. Dividing them gives [M L² T⁻³].

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