The method of dimensional analysis can be used to derive which of relation?

Options

A. `A sin (omega t- kx)`
B. `N_(o)e^(- lamda t)`
C. `b log ((a)/(lamda))`
D. `F= 6pi eta rv`

Answer

To solve the question regarding which relation can be derived using dimensional analysis, we can follow these steps:

### Step 1: Understand Dimensional Analysis
Dimensional analysis is a method used in physics to derive relationships between physical quantities by analyzing their dimensions. It helps in checking the consistency of equations and deriving formulas.

### Step 2: Identify Limitations of Dimensional Analysis
Dimensional analysis cannot be used to derive relationships that involve:
- Logarithmic terms (e.g., log(x))
- Exponential terms (e.g., e^x)
- Trigonometric terms (e.g., sin(x), cos(x))

### Step 3: Analyze the Options
Given the options (A, B, C, D), we need to identify which one contains a term that is not subject to the limitations of dimensional analysis:
- Option A: Contains a trigonometric term
- Option B: Contains an exponential term
- Option C: Contains a logarithmic term
- Option D: Contains no such terms

### Step 4: Conclusion
Since options A, B, and C all include terms that cannot be analyzed using dimensional analysis, the only option that does not contain any of these terms is option D. Therefore, the correct answer is:

**Answer: Option D**