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Assertion
A dimensionally wrong or inconsistent equation must be wrong.
Reason
A dimensionally consistent equation is an exact or a correct equation.
A. Both assertion and Reason are correct and Reason is the correct explanation for assertion.
B. Both assertion and reason are correct but reason is not the correct explanation for assertion.
C. Assertion is correct but reason is incorrect.
D. Both assertion and reason are incorrect.

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Last updated date: 16th Jun 2024
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Answer
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Hint: In order for you to answer this question, you should be very thorough with the concept of dimension and dimensional analysis. Recall how we can check the dimensional consistency of an equation. Also, recall that there are quantities which are dimensionless and their presence isn’t detected during this analysis.

Complete solution:
In the question, we are given an assertion and reason related to dimensional analysis. In order to answer this question, we will have to know what exactly the dimensional analysis is.
Dimension of a physical quantity could be defined as the power to which that quantity is raised in order to represent that quantity. It is possible for us to check the dimensional consistency of an equation. We use the principle of homogeneity to do that.

An equation is said to be dimensionally correct when the dimension on both sides of the equation is the same. Otherwise, the equation is said to be dimensionally wrong.
For example, if we derive a relation of speed, for the relation to be dimensionally correct the dimension on both sides should be that of speed, that is,$\left[ L{{T}^{-1}} \right]$
We could use this consistency test in order to prove an equation wrong. Any equation that fails this test is proved wrong. However, a dimensionally correct equation cannot be considered as a correct equation.

Therefore, we found that the assertion is a true statement while the reason is a false statement.

Hence, option C is the correct answer.

Note:
A dimensionally correct equation cannot be considered as the correct equation due to various reasons. The uncertainty of the presence of dimensionless quantities and functions is an important factor. Trigonometric, logarithmic and exponential functions are dimensionless. A pure number and the ratio of similar physical quantities are also dimensionless.