Write the SI unit of volumetric strain.

Answer

To find the SI unit of volumetric strain, we can follow these steps:

### Step 1: Understand the Definition of Strain
Strain is defined as the ratio of change in a physical dimension to the original dimension. It can be expressed mathematically as:
\[ \text{Strain} = \frac{\text{Change in Dimension}}{\text{Original Dimension}} \]

### Step 2: Identify the Type of Strain
There are three types of strain:
1. Longitudinal strain
2. Volumetric strain
3. Shear strain

In this case, we are focusing on volumetric strain.

### Step 3: Write the Formula for Volumetric Strain
Volumetric strain is defined as the change in volume divided by the original volume:
\[ \text{Volumetric Strain} = \frac{\Delta V}{V_0} \]
where \( \Delta V \) is the change in volume and \( V_0 \) is the original volume.

### Step 4: Determine the Units of Volume
The SI unit of volume is cubic meters (m³). Therefore, the unit of change in volume (\( \Delta V \)) is also in cubic meters (m³).

### Step 5: Calculate the Units of Volumetric Strain
Substituting the units into the formula for volumetric strain, we have:
\[ \text{Volumetric Strain} = \frac{\text{Change in Volume (m³)}}{\text{Original Volume (m³)}} \]

### Step 6: Simplify the Units
When we divide the change in volume by the original volume, the cubic meters cancel out:
\[ \text{Volumetric Strain} = \frac{m³}{m³} = 1 \]

### Conclusion
Since volumetric strain is a ratio of two volumes, it is a dimensionless quantity. Therefore, the SI unit of volumetric strain is unitless.

### Final Answer
The SI unit of volumetric strain is dimensionless (unitless).

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