A circular disc is to be made by using iron and aluminium, so that it acquires maximum moment of inertia about its geometrical axis. It is possible with

Options

A. aluminimum is at the interior and iron surrounds it
B. iron is at the interior and aluminimum surrrounds it
C. aluminium and iron layers are in alternate order
D. sheet of iron is used at both external surfaces and aluminium sheet as inner material

Answer

To solve the problem of maximizing the moment of inertia of a circular disc made from iron and aluminum, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Moment of Inertia**:
The moment of inertia (I) of a body about an axis is given by the formula:
\[ I = \sum m_i r_i^2 \]
where \(m_i\) is the mass of each particle and \(r_i\) is the distance from the axis of rotation.

2. **Identify the Materials**:
We have two materials: iron and aluminum. We need to consider their densities and how they will be arranged in the disc.

3. **Compare Densities**:
Iron is denser than aluminum. This means that for the same volume, iron will have a greater mass than aluminum.

4. **Maximize Moment of Inertia**:
To maximize the moment of inertia, we want to place the heavier material (iron) at a greater distance from the axis of rotation. This is because the moment of inertia increases with the square of the distance from the axis (\(r^2\)).

5. **Arrangement of Materials**:
To achieve maximum moment of inertia, we should place aluminum (the lighter material) closer to the center and iron (the heavier material) further away from the center.

6. **Conclusion**:
Therefore, the correct arrangement is to have aluminum in the interior and iron surrounding it.

### Final Answer:
The correct option is that aluminum is in the interior and iron surrounds it.