A dimensionally correct equation means that the units on both sides of the equation are consistent and match in terms of dimensions. However, a dimensionally correct equation does not guarantee that it is a correct physical relation or that it accurately describes the behavior or relationship between the quantities involved.
In physics, dimensional analysis is a powerful tool for checking the consistency of equations and identifying potential errors or inconsistencies. By examining the dimensions of various quantities in an equation, you can determine if the equation makes sense from a dimensional standpoint. If the dimensions on both sides of the equation match, it suggests that the equation could be physically valid, but it does not prove its correctness.
It is possible to have dimensionally correct equations that are based on incorrect assumptions or incorrect physical principles. In such cases, the equation may give results that seem consistent with dimensions but do not accurately reflect the true behavior or relationship between the quantities being studied.
On the other hand, a dimensionally wrong equation, where the units on both sides of the equation do not match, typically indicates a fundamental error or inconsistency in the equation. Such equations are generally not considered valid or physically meaningful.
Therefore, while dimensional analysis is a valuable tool for checking the consistency of equations and identifying potential errors, it is essential to go beyond just dimensional considerations and rigorously analyze the underlying physical principles, assumptions, and experimental evidence to determine the correctness and validity of a physical relation or equation.