In materials like aluminium and copper, the correct order of magnitude of various elastic moduli is:

Answer

To solve the problem regarding the order of magnitude of various elastic moduli for materials like aluminum and copper, we will follow these steps:

### Step 1: Understand the Elastic Moduli
The three main types of elastic moduli are:
1. **Young's Modulus (Y)** - It measures the stiffness of a material.
2. **Shear Modulus (G)** - It measures the material's response to shear stress.
3. **Bulk Modulus (B)** - It measures the material's response to uniform pressure.

### Step 2: Write the Relationships
The relationships between these moduli can be expressed as follows:
- **Shear Modulus (G)**: \( G = \frac{Y}{2(1 + \mu)} \)
- **Bulk Modulus (B)**: \( B = \frac{Y}{3(1 - 2\mu)} \)

Where \( \mu \) is the Poisson's ratio.

### Step 3: Determine Poisson's Ratio
For materials like aluminum and copper, the Poisson's ratio (\( \mu \)) is approximately 0.3.

### Step 4: Calculate the Moduli
Using the Poisson's ratio, we can substitute it into the formulas for \( G \) and \( B \):
1. **Calculate Bulk Modulus (B)**:
\[ B = \frac{Y}{3(1 - 2 \times 0.3)} = \frac{Y}{3(1 - 0.6)} = \frac{Y}{3 \times 0.4} = \frac{Y}{1.2} \]

2. **Calculate Shear Modulus (G)**:
\[ G = \frac{Y}{2(1 + 0.3)} = \frac{Y}{2 \times 1.3} = \frac{Y}{2.6} \]

### Step 5: Compare the Values
From the calculations:
- \( G = \frac{Y}{2.6} \)
- \( B = \frac{Y}{1.2} \)

### Step 6: Establish the Order
Since \( G < Y < B \):
- Shear Modulus (G) is the smallest,
- Young's Modulus (Y) is in the middle,
- Bulk Modulus (B) is the largest.

### Conclusion
The correct order of magnitude of the elastic moduli for materials like aluminum and copper is:
\[ G < Y < B \]