A uniform cube is subjected to volume compression. If each side is decreased by `1%`, then bulk strain is

Options

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

Explanation

To solve the problem of finding the bulk strain when a uniform cube is subjected to volume compression with each side decreased by 1%, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Bulk Strain**:
Bulk strain (also known as volumetric strain) is defined as the change in volume (ΔV) divided by the original volume (V). Mathematically, it is expressed as:
\[ \text{Bulk Strain} = \frac{\Delta V}{V} \]

2. **Determine the Volume of the Cube**:
The volume (V) of a cube with side length (A) is given by:
\[ V = A^3 \]

3. **Calculate the Change in Volume**:
If each side of the cube is decreased by 1%, the new side length becomes:
\[ A' = A - 0.01A = 0.99A \]
The new volume (V') of the cube after compression is:
\[ V' = (A')^3 = (0.99A)^3 = 0.99^3 A^3 \]
Now, we can calculate ΔV:
\[ \Delta V = V' - V = 0.99^3 A^3 - A^3 = (0.99^3 - 1) A^3 \]

4. **Calculate the Value of 0.99^3**:
We can calculate \(0.99^3\):
\[ 0.99^3 \approx 0.970299 \]
Therefore,
\[ \Delta V = (0.970299 - 1) A^3 = -0.029701 A^3 \]

5. **Calculate the Original Volume**:
The original volume (V) is:
\[ V = A^3 \]

6. **Substitute into the Bulk Strain Formula**:
Now we can substitute ΔV and V into the bulk strain formula:
\[ \text{Bulk Strain} = \frac{\Delta V}{V} = \frac{-0.029701 A^3}{A^3} = -0.029701 \]

7. **Express Bulk Strain as a Positive Value**:
Since strain is typically expressed as a positive value, we take the absolute value:
\[ \text{Bulk Strain} \approx 0.029701 \approx 0.03 \]

### Final Answer:
The bulk strain when each side of the cube is decreased by 1% is approximately **0.03**.

---