If n is the numerical value of a physical quantity in the system in which its unit is u. then which of the following relations is correct?

Options

A. `n/u`=constant
B. `u/n`=constant
C. nu=constant
D. `n^2u`=constant

Answer

To solve the problem, we need to understand the relationship between the numerical value \( n \) of a physical quantity and its unit \( u \). Let's break down the solution step by step:

### Step 1: Understand the relationship between numerical value and unit
When we express a physical quantity, it can be represented as:
\[ \text{Physical Quantity} = n \cdot u \]
where \( n \) is the numerical value and \( u \) is the unit.

### Step 2: Consider an example
Let's take an example of mass. Suppose we have a mass of 50 kg. Here, \( n = 50 \) and \( u = \text{kg} \).

### Step 3: Convert the unit
We can convert kilograms to grams:
\[ 50 \text{ kg} = 50 \times 1000 \text{ g} = 50000 \text{ g} \]
In this case, the numerical value \( n \) has increased (from 50 to 50000), while the unit has changed from kg to g.

### Step 4: Analyze the effect of unit conversion
Now, let's consider another conversion. If we convert 50 kg to quintals:
\[ 50 \text{ kg} = 0.5 \text{ quintals} \]
Here, the numerical value \( n \) has decreased (from 50 to 0.5), while the unit has changed from kg to quintals.

### Step 5: Establish the relationship
From the examples, we can see that as the numerical value \( n \) increases, the unit \( u \) decreases, and vice versa. This implies that \( n \) and \( u \) are inversely proportional to each other.

### Step 6: Write the mathematical relation
We can express this relationship mathematically as:
\[ n \cdot u = \text{constant} \]
This means that the product of the numerical value and the unit remains constant regardless of the unit system used.

### Conclusion
Thus, the correct relation that describes the relationship between the numerical value \( n \) and the unit \( u \) is:
\[ n \cdot u = \text{constant} \]
Therefore, the correct answer to the question is option C.

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