A uniform cube is subjected to volume compression. If each side is decreased by 3%, the bulk strain is

Options

A. `27%`
B. `8%`
C. `9%`
D. `1%`

Explanation

To solve the problem of finding the bulk strain when each side of a uniform cube is decreased by 3%, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**:
- We have a uniform cube with each side length denoted as \( L \).
- Each side of the cube is decreased by 3%.

2. **Calculate the New Side Length**:
- The new side length after a decrease of 3% can be calculated as:
\[ L' = L - 0.03L = 0.97L \]

3. **Calculate the Original Volume**:
- The original volume \( V \) of the cube is given by:
\[ V = L^3 \]

4. **Calculate the New Volume**:
- The new volume \( V' \) after the side length is decreased is:
\[ V' = (L')^3 = (0.97L)^3 = 0.97^3 L^3 \]
- Now, calculate \( 0.97^3 \):
\[ 0.97^3 \approx 0.912673 \]
- Therefore, the new volume is:
\[ V' \approx 0.912673 L^3 \]

5. **Calculate the Change in Volume**:
- The change in volume \( \Delta V \) is given by:
\[ \Delta V = V' - V = 0.912673 L^3 - L^3 = (0.912673 - 1)L^3 = -0.087327 L^3 \]

6. **Calculate the Bulk Strain**:
- Bulk strain is defined as the change in volume divided by the original volume:
\[ \text{Bulk Strain} = \frac{\Delta V}{V} = \frac{-0.087327 L^3}{L^3} = -0.087327 \]
- To express this as a percentage, we multiply by 100:
\[ \text{Bulk Strain} \approx -8.73\% \]

### Final Answer:
The bulk strain when each side of the cube is decreased by 3% is approximately **8.73%**.