What are the principles for ensuring the consistency of an equation through dimensional analysis? Statement I: The sum of all exponents of any dimension (e.g., mass), should be the same on both sides of the equation. Statement II: An exponent must itself be a pure / dimensionless number. Statements III: The magnitude of the exponent does not necessarily have to be a whole number.
What are the principles for ensuring the consistency of an equation through dimensional analysis? Statement I: The sum of all exponents of any dimension (e.g., mass), should be the same on both sides of the equation. Statement II: An exponent must itself be a pure / dimensionless number. Statements III: The magnitude of the exponent does not necessarily have to be a whole number. Correct Answer I, II & III
To verify the correctness of any given equation through dimensional analysis, we need to ensure that the sums of all exponents relating to any given dimension are equal on both sides of the equation. The exponent should be dimensionless or in other words, a pure number, although its magnitude does not necessarily have to be a whole number.
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Feb 20, 2025