Question

if an equation is dimesnsionally corrext does that the equation must be zero?

Answer 1

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A dimensionally incorrect equation is something like asking to add mangoes and oranges to get apples! Dimensions are what make a quantifiable entity, and in the rules of classical Physics, they are the very basis of life. You can not add velocity with acceleration and because a 'time' dimension starts pouting, and this upsets Physics!

Seriously though, if you are writing any equation, be it of time and motion or chemical equations, the thing to bear in mind is that the input and output should be balanced, not only in quantity, but also in nature. This regulation also helps in a number of ways. It helps writing equation, hassle free and also gives us a assurance that since they are dimensionally coherent, they should be correct.

Now, a true equation must also be dimensionally correct but its not necessary that all dimensionally correct equations are true.

For example, area of a square is (side)^2, which is true. but if someone says that area is 2* (side)^2, he is not correct(obviously). You see, both the equations are dimensionally correct, but the second one of false.

Therefore a dimensionally correct equation may or may not be correct, but a dimensionally incorrect equation is necessarily a WRONG physical equation.

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