The S.I. unit of compressibility is

Options

A. Pa
B. `Pa^(-1)`
C. `N//m`
D. `m//N`

Answer

To determine the S.I. unit of compressibility, we can follow these steps:

### Step 1: Understand the Definition of Compressibility
Compressibility (denoted as \( k \)) is defined as the measure of the relative change in volume of a material in response to a change in pressure. Mathematically, it is given by:

\[ k = \frac{1}{B} \]

where \( B \) is the bulk modulus of the material.

### Step 2: Understand the Bulk Modulus
The bulk modulus \( B \) is defined as:

\[ B = -\frac{P}{\Delta V/V} \]

where:
- \( P \) is the change in pressure,
- \( \Delta V \) is the change in volume,
- \( V \) is the original volume.

### Step 3: Rearranging the Formula
From the definition of compressibility:

\[ k = \frac{\Delta V/V}{P} \]

### Step 4: Identify the Units
Now, let's identify the units involved:
- The change in volume \( \Delta V \) has units of \( \text{m}^3 \).
- The original volume \( V \) also has units of \( \text{m}^3 \).
- Therefore, the ratio \( \Delta V/V \) is dimensionless.
- The pressure \( P \) has units of Pascal (Pa), which can be expressed as \( \text{N/m}^2 \) or \( \text{kg/(m \cdot s}^2) \).

### Step 5: Calculate the Units of Compressibility
Since compressibility \( k \) is defined as:

\[ k = \frac{\Delta V/V}{P} \]

The unit of compressibility can be derived as follows:

\[ \text{Unit of } k = \frac{1}{\text{Unit of } P} = \frac{1}{\text{Pa}} = \frac{1}{\text{N/m}^2} = \frac{\text{m}^2}{\text{N}} \]

### Step 6: Final Answer
Thus, the S.I. unit of compressibility is:

\[ \text{m}^2/\text{N} \]