Dimensional Analysis

Classical Mechanics Level 2

The dimensional formula of Electrical energy can be represented as M w L x T y A z M^{w}L^{x}T^{y}A^{z} , where M M stands for mass, L L stands for length, T T stands for time and A A stands for Ampere. What is w + x + y + z w + x + y + z ?


The answer is 1.

Ashish Menon by Ashish Menon , 20, India

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1 solution

Ashish Menon
Apr 28, 2016

Electrical energy is an energy which is Force × Displacement. Now Force = Mass × Acceleration. Now, acceleration = Velocity / Time. Now velocity = Displacement / Time.
So, dimensional formula of velocity = L T − 1 LT^{-1}
So, dimensional formula of acceleration = L T − 2 LT^{-2}
So, dimensional formula of force = L 2 T − 2 L^{2}T^{-2}
So, dimensional formula of energy = M L 2 T − 2 ML^{2}T^{-2}


It can be represented as M 1 L 2 T − 2 A 0 M^{1}L^{2}T^{-2}A^{0}
So, w + x + y + z = 1 + 2 − 2 + 0 = 1 w + x + y + z = 1 + 2 - 2 + 0 = \boxed{1}

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I made a question for ya. Check it!

Abhiram Rao - 5 years, 1 month ago

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Thanks Abhiram, your question was fun solving :+1: I would post a solution soon :)

Ashish Menon - 5 years, 1 month ago

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