On the basis of dimensional equation, the maximum number of unknown that can be found, is

Options

A. one
B. two
C. three
D. four

Answer

To determine the maximum number of unknowns that can be found using dimensional analysis, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Fundamental Dimensions**:
The fundamental dimensions in physics are mass (M), length (L), and time (T). These are the basic building blocks for dimensional analysis.

2. **Understand Dimensional Equations**:
Any physical quantity can be expressed in terms of these three fundamental dimensions. For example, the dimensional formula for force is [F] = [M^1 L^1 T^-2].

3. **Set Up Equations**:
When you have a physical relationship involving several unknowns, you can set up equations based on the dimensional formulas. Each dimension (M, L, T) can be equated separately.

4. **Count the Equations**:
Since there are three fundamental dimensions, you can form three independent equations by equating the dimensions of both sides of the equation.

5. **Solve for Unknowns**:
Each independent equation can help solve for one unknown. Therefore, with three independent equations, you can solve for a maximum of three unknowns.

6. **Conclusion**:
Based on this reasoning, the maximum number of unknowns that can be determined using dimensional analysis is three.

### Final Answer:
The maximum number of unknowns that can be found on the basis of dimensional equations is **3**.

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