If n is number and u is the unit of a physical quantity then which of the following is correct for the measurement of "n".

Options

A. `n prop ` size of u
B. `n prop u^2`
C. `n prop sqrt(u)`
D. `n prop 1/u`

Explanation

To solve the question, we need to analyze the relationship between the number \( n \) and the unit \( u \) of a physical quantity.

### Step-by-Step Solution:

1. **Understanding the Representation of Physical Quantity**:
- A physical quantity can be expressed as the product of a number and its unit. This can be represented as:
\[ \text{Physical Quantity} = n \cdot u \]
- Here, \( n \) is the numerical value, and \( u \) is the unit of measurement.

2. **Establishing the Relationship**:
- Since the physical quantity is constant, we can denote it as \( C \):
\[ n \cdot u = C \]
- This implies that the product of the number and the unit is a constant value.

3. **Expressing \( n \) in Terms of \( u \)**:
- Rearranging the equation gives us:
\[ n = \frac{C}{u} \]
- This shows that \( n \) is inversely proportional to \( u \).

4. **Conclusion**:
- From the relationship derived, we can conclude that:
\[ n \propto \frac{1}{u} \]
- Therefore, the correct answer is that \( n \) is proportional to the inverse of \( u \).

### Final Answer:
- The correct option is: \( n \) is proportional to the inverse of \( u \).

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