N. `m^(-1)` is the S.I unit of

Options

A. Force constant
B. Spring constant
C. Surface tension
D. 1,2 and 3

Answer

To solve the question regarding what N. m^(-1) represents as an SI unit, we can follow these steps:

### Step 1: Understand the Unit
The unit N. m^(-1) can be broken down into its components:
- N (Newton) is the SI unit of force.
- m^(-1) indicates per meter, which suggests a relationship with length.

### Step 2: Analyze the Possible Options
We have the following options:
1. Force constant
2. Spring constant
3. Surface tension
4. Options 1, 2, and 3

### Step 3: Relate the Unit to Each Option
- **Force Constant**: This is often synonymous with the spring constant (k). The spring constant is defined as the force required to compress or extend a spring by a unit length. Mathematically, it is expressed as:
\[ k = \frac{F}{x} \]
where \( F \) is the force in Newtons and \( x \) is the displacement in meters. Thus, the unit of spring constant \( k \) is N. m^(-1).

- **Spring Constant**: As mentioned above, the spring constant (k) is indeed measured in N. m^(-1). This confirms that the spring constant is represented by the unit N. m^(-1).

- **Surface Tension**: Surface tension is defined as the force acting along the surface of a liquid per unit length. It is calculated as:
\[ \text{Surface Tension} = \frac{F}{L} \]
where \( F \) is the force in Newtons and \( L \) is the length in meters. Therefore, the unit of surface tension is also N. m^(-1).

### Step 4: Conclusion
Since all three options (force constant, spring constant, and surface tension) can be expressed in the unit N. m^(-1), the correct answer is:
**Option 4: Options 1, 2, and 3.**