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 understand the relationship between the numerical values and units of a physical quantity in two different systems of units.

### Step-by-Step Solution:

1. **Understanding the Physical Quantity**:
- A physical quantity can be expressed as the product of a numerical value and a unit. This can be represented as:
\[ PQ = n \cdot u \]
- Where \( PQ \) is the physical quantity, \( n \) is the numerical value, and \( u \) is the unit.

2. **Setting Up the Equation**:
- For two different systems of units, we have:
- In the first system: \( n_1 \) and \( u_1 \)
- In the second system: \( n_2 \) and \( u_2 \)
- Therefore, we can write:
\[ n_1 \cdot u_1 = n_2 \cdot u_2 \]

3. **Understanding the Relationship**:
- This equation indicates that the product of the numerical value and the unit remains constant when switching between different units for the same physical quantity.
- This means that if you change the unit, the numerical value will change in such a way that their product remains the same.

4. **Conclusion**:
- Thus, we can conclude that:
\[ n_1 \cdot u_1 = n_2 \cdot u_2 \]
- This relationship shows that if one unit is larger, the corresponding numerical value will be smaller, and vice versa.

### Final Answer:
\[ n_1 \cdot u_1 = n_2 \cdot u_2 \]

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