A uniform cube is subjected to volume compression. If each side is decreased by 2% , then bulk strain is

Options

A. 0.01
B. 0.03
C. 0.02
D. 0.06

Explanation

To solve the problem of finding the bulk strain when a uniform cube is subjected to volume compression with each side decreased by 2%, we can follow these steps:

### Step 1: Understand the Definitions
- **Bulk Strain (ε)** is defined as the change in volume (ΔV) divided by the original volume (V). Mathematically, it is expressed as:
\[ \text{Bulk Strain} = \frac{\Delta V}{V} \]

### Step 2: Determine the Change in Length
- The problem states that each side of the cube is decreased by 2%. This can be expressed as:
\[ \Delta L = -0.02L \]
where \(L\) is the original length of a side of the cube.

### Step 3: Calculate the Original Volume
- The volume \(V\) of a cube is given by:
\[ V = L^3 \]

### Step 4: Calculate the New Volume
- After the side length is decreased, the new length of each side becomes:
\[ L' = L - \Delta L = L - 0.02L = 0.98L \]
- The new volume \(V'\) can be calculated as:
\[ V' = (L')^3 = (0.98L)^3 = 0.98^3 L^3 \]

### Step 5: Calculate the Change in Volume
- The change in volume (ΔV) is given by:
\[ \Delta V = V' - V = 0.98^3 L^3 - L^3 \]
- Simplifying this, we have:
\[ \Delta V = (0.98^3 - 1)L^3 \]

### Step 6: Calculate the Bulk Strain
- Now, substituting ΔV into the bulk strain formula:
\[ \text{Bulk Strain} = \frac{\Delta V}{V} = \frac{(0.98^3 - 1)L^3}{L^3} = 0.98^3 - 1 \]
- Calculating \(0.98^3\):
\[ 0.98^3 \approx 0.941192 \]
- Therefore:
\[ \text{Bulk Strain} = 0.941192 - 1 \approx -0.058808 \]

### Step 7: Express the Bulk Strain as a Positive Value
- Since strain is often expressed as a positive value, we take the absolute value:
\[ \text{Bulk Strain} \approx 0.0588 \text{ or } 5.88\% \]

### Conclusion
The bulk strain when each side of the cube is decreased by 2% is approximately **0.0588** or **5.88%**.