If an equation is dimensionally correct, does this mean that the equation must be true? If an equation is not dimensionally correct, does this mean that the equation cannot be true? How is dimension analysis used as a check on the plausibiity of derived equations and computations? How does this knowledge help you to understand and characterize particular phenomenon? Explain.

answer: A dimensionally correct equation deosn't make the equation true. It is always possible to construct an arbitrary meaningless equation that satisfies the dimensional analysis. we can observe this in different physical quantities that have the same dimensional formula, by inserting a wrong physical parameter into an equation, it may turn out as dimensionally correct, but it wont have any physical meaning.

If an equation is not dimensionally correct, does this mean that the equation cannot be true?

answer: A dimensionally incorrect equation necessarily implies that the equation is wrong.

How is dimension analysis used as a check on the plausibiity of derived equations and computations?

answer: dimensional analysis is a very strong tool that is used to check the trustworthiness of a derived equation. It helps to compare the dimensions of the output variable from an equation against the true dimensions of the output variable. If both of them are not same, the equation/computation/derivation is incorrect.

How does this knowledge help you to understand and characterize particular phenomenon?

answer: the knowledge of dimensional analysis helps in understanding which variables are necessary for defining a process.