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You do the calculations, not with actual numbers, but with dimensions. For example, [length] + [length] = [length], [length] x [length] = [length]2, square root of [time]4 = [time]2, etc. In the final result, left and right of the equation have to be equal. For more information, search about dimensional analysis (for example, the Wikipedia article on dimensional analysis might help).

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Q: How can you tell if an equation is dimensionally correct?
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Related questions

A dimensionally incorrect equation may be correct?

no it can't be


Is dimensionally correct equations necessarily be a physical relation?

No, not all dimensionally correct equations represent physical relationships. Dimensional analysis focuses on the units of measurements in an equation to ensure consistency but does not guarantee the physical relevance of the relationship itself. It is possible to have dimensionally correct equations that do not have a meaningful physical interpretation.


You are told that the volume of an object of unknown shape is given by V equals where V is the volume and d is the diameter of the sphere Is this equation dimensionally correct?

Circle.


What do you mean when you say the that an equation is dimensionally correct?

It means that the dimensions of all terms agree with the basic rules of mathematical operations. It also means that only terms with the same dimensions are added or subtracted.


Is the equation 8kg 4kg 12kgs dimensionally correct?

Unfortunately, the browser used for posting questions is hopelessly inadequate for mathematics: it strips away most symbols. It is, therefore, impossible to be certain, but I suspect that the answer is yes.


Is mass times acceleration equals velocity squared dimensionally correct?

No, mass times acceleration does not equal velocity squared dimensionally. The dimensional equation for mass times acceleration is [M][L][T]^-2, while the dimensional equation for velocity squared is [L]^2[T]^-2. These are not equivalent dimensions.


Is it true that dimensional analysis can tell whether an equation is physically correct?

yes


Which is the correct set of coefficient for the equation below?

The correct set of coefficient for an equation depends with the equation in question. There are many types of equations.


What is Planck's constant dimensionally equal to?

Planck's Constant is dimensionally equal to Angular Momentum. The unit is Joules second.


What are the disadvantages of oblique cavalier drawings?

Oblique cavalier drawings tend to appear distorted and elongated. They are not considered as true projections despite being dimensionally correct.


Can you tell how a quadratic equation can become linear equation?

You can easily tell by substituting 0 for a.


What is mathematically complete?

if an equation is given the correct answer, it is mathematically correct.