The numerical values and units of a physical quantity in two different system of units are `n_(1), n_(2) and u_(1), u_(2)` respectively. Then

Options

A. `n_(1)u_(2)=n_(2)u_(1)`
B. `n_(1)u_(1)^(2)=n_(2)u_(2)^(2)`
C. `n_(1)=n_(2) & u_(1)=u_(2)`
D. `n_(1)u_(1)=n_(2)u_(2)`

Answer

To solve the problem, we need to establish the relationship between the numerical values and units of a physical quantity in two different systems of units. Let's denote the numerical values as \( n_1 \) and \( n_2 \) and the corresponding units as \( u_1 \) and \( u_2 \).

### Step-by-Step Solution:

1. **Understanding the Physical Quantity**:
- We have a physical quantity that can be expressed in two different systems of units. For instance, if we consider length, we can express it in meters (m) and centimeters (cm).

2. **Setting Up the Relationship**:
- In any system of units, the physical quantity can be represented as:
\[ \text{Physical Quantity} = n_1 \times u_1 \]
for the first system, and
\[ \text{Physical Quantity} = n_2 \times u_2 \]
for the second system.

3. **Equating the Two Expressions**:
- Since both expressions represent the same physical quantity, we can set them equal to each other:
\[ n_1 \times u_1 = n_2 \times u_2 \]

4. **Deriving the Final Relationship**:
- Rearranging the equation gives us the relationship between the numerical values and units:
\[ n_1 u_1 = n_2 u_2 \]

5. **Conclusion**:
- Thus, the relationship between the numerical values and units of the physical quantity in the two different systems is given by:
\[ n_1 u_1 = n_2 u_2 \]

### Final Answer:
The relationship is \( n_1 u_1 = n_2 u_2 \).

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