Choose the incorrect statement:A. A dimensionally correct equation may be correct.B. A dimensionally correct equation may be incorrect.C. A dimensionally incorrect equation must be incorrect.D. A dimensionally incorrect equation may be correct.
Answers
We know that if we want to validate an equation then both its LHS and RHS must be having the same dimension. In Layman's term one can never compare apples with bananas or oranges. In order to compare both must be the same fruit.
Similar is the case with the equations. Now in this question, we have four statements out of which 1 is incorrect.
The first three statements are true.
Option A is true because it is not mandatory that a dimensionally correct equation must be valid. eg: area of a circle = 2 x radius^2 This is correct dimensionally, but there must be pi in place of 2.
If this can be the case then it is pretty obvious that a dimensionally incorrect equation can never be valid.
Therefore the fourth statement is wrong.
Answer ⇒ Option (D). A dimensionally incorrect equation may be correct.
Explanation ⇒
A dimensionally equation does not involves the number and if the methods of the dimensions are applied to check the correctness of the equation it does not involves the pure numbers and dimensionless constant. Trigonometrical Ratios and the Logarithms functions are all dimensionless.
We can say that all the equations which are correct must be dimensionally correct but all those which are incorrect may or may not be dimensionally correct.
Also, All those equation which are dimensionally correct may or may not accurately correct.
Thus, Option (a), (b) and (c) are correct statements thus they cannot be the answer of the given question.
Hence, Option D is correct answer.
Hope it helps. :-)