Question

Choose the correct statement(s).
A. A dimensionally correct equation must be correct.
B. A dimensionally correct equation may be correct.
C. A dimensionally incorrect equation must be incorrect.
D. A dimensionally incorrect equation may be correct.

Answer 1

Hint: In this question, we need to determine the correct option(s) out of the given options. For this, we will be using the principle of homogeneity of dimension to identify the correct statement(s).

Complete step by step solution:
First, we will discuss the concept of dimensional equations. Dimensional equations are equations that include physical quantities and dimensional formulas.

Let us now look at the dimensional homogeneity principle. An equation is practically valid when it becomes dimensionally correct, according to the concept of dimension homogeneity.That means that the dimensions of every term in a dimensional equation on both sides should be the same.

So when the equation is dimensionally inaccurate, it will be physically incorrect. Therefore, statements like “A dimensionally correct equation may be correct” and “A dimensionally incorrect equation may be correct” are correct.

Hence, the options (B) and (D) are correct.

Additional Information: The analysis of the relationship between physical quantities based on their units as well as dimensions is known as dimensional analysis. That is, it is a methodology in which physical values are described in terms of their basic dimensions, frequently utilised whenever there is insufficient data to draw up accurate equations.

Note:We can also identify correct statements by taking examples. The example of statement (b) is \[s = ut + a{t^2}\]. This equation is dimensionally correct but actually it is incorrect. Also, the example of statement (d) is \[s = u + \dfrac{a}{2}\left( {2n - 1}
\right)\]. This equation is correct but dimensionally incorrect.