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 solve the question about the maximum number of unknowns that can be found based on dimensional equations, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Dimensional Analysis**:
- Dimensional analysis involves expressing physical quantities in terms of fundamental dimensions: Mass (M), Length (L), and Time (T).

2. **Identifying the Fundamental Dimensions**:
- The fundamental dimensions are M (mass), L (length), and T (time). These are the basic building blocks for any physical quantity.

3. **Formulating the Dimensional Equation**:
- When we express a physical quantity (let's say A) in terms of its dimensions, we can represent it as:
\[ A = M^a \cdot L^b \cdot T^c \]
- Here, \(a\), \(b\), and \(c\) are the powers corresponding to the dimensions of mass, length, and time, respectively.

4. **Maximum Number of Unknowns**:
- In a dimensional equation, we can have at most three different dimensions (M, L, T). Therefore, we can assign unknown powers \(a\), \(b\), and \(c\) to these three dimensions.
- Since each dimension can be treated as an independent variable, we can solve for a maximum of three unknowns.

5. **Conclusion**:
- Thus, the maximum number of unknowns that can be determined using dimensional analysis is **3**.

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

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