A physical quantity is measured and the result is expressed as nu where u is the unit used and n is the numberical value. If the result is expressed in various units then

Options

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

Answer

To solve the problem, we need to understand the relationship between the numerical value (n) and the unit (u) when a physical quantity is expressed in different units.

### Step-by-Step Solution:

1. **Understanding the Expression**:
The physical quantity is expressed as \( n \cdot u \), where \( n \) is the numerical value and \( u \) is the unit.

2. **Example of Measurement**:
Let's take an example where we measure a length and find it to be 1 meter. Here, \( n = 1 \) and \( u = \text{meter} \).

3. **Conversion to Different Units**:
- Convert 1 meter to millimeters:
\[ 1 \text{ meter} = 1000 \text{ mm} \]
Here, \( n = 1000 \) and \( u = \text{mm} \).

- Convert 1 meter to kilometers:
\[ 1 \text{ meter} = 0.001 \text{ km} \]
Here, \( n = 0.001 \) and \( u = \text{km} \).

4. **Observing the Changes**:
- When we converted from meters to millimeters, the numerical value increased from 1 to 1000, while the unit changed from meters to millimeters (a smaller unit).
- When we converted from meters to kilometers, the numerical value decreased from 1 to 0.001, while the unit changed from meters to kilometers (a larger unit).

5. **Conclusion**:
From the conversions, we can observe that as the size of the unit \( u \) increases (from mm to m to km), the numerical value \( n \) decreases. This indicates that the numerical value \( n \) is inversely proportional to the size of the unit \( u \).

6. **Final Answer**:
Therefore, we conclude that:
\[ n \propto \frac{1}{u} \]
This means that \( n \) is inversely proportional to \( u \).