Statement - 1 : Let `I_(1) and I_(2)` be the moment of inertia of two bodies of identical geometrical shapes, the first made of aluminium and second of iron then `I_(1) lt I_(2)`. Becaause
Statement - 2 : Moment of inertia does not depends on shape

Options

A. Statement - 1 is true, statement - 2 is true, statement - 2 is correct explanation for statement - 1
B. Statement - 1 is true, Statement - 2 is true, Statement - 2 is not a correct explanation for statement - 1
C. statement - 1 is true, statement - 2 is false
D. statement - 1 is false, statement - 2 is true.

Answer

To analyze the statements given in the question, we will break down the reasoning step by step.

### Step 1: Understanding Moment of Inertia
The moment of inertia (I) of a body is defined as the sum of the products of the mass of each particle of the body and the square of its distance from the axis of rotation. The formula can be expressed as:
\[ I = \sum m_i r_i^2 \]
where \( m_i \) is the mass of each particle and \( r_i \) is the distance from the axis of rotation.

### Step 2: Analyzing Statement 1
Statement 1 claims that the moment of inertia \( I_1 \) of the aluminum body is less than the moment of inertia \( I_2 \) of the iron body, i.e., \( I_1 < I_2 \).

- Both bodies are of identical geometrical shapes, meaning they have the same dimensions.
- The moment of inertia depends on both the mass and the distribution of mass relative to the axis of rotation.
- Since aluminum has a lower density than iron, for the same volume (and hence the same shape), the mass of the aluminum body will be less than that of the iron body.
- Therefore, since \( I \) is directly proportional to mass (for identical shapes), we conclude that:
\[ I_1 < I_2 \]
Thus, Statement 1 is **true**.

### Step 3: Analyzing Statement 2
Statement 2 claims that the moment of inertia does not depend on shape.

- This statement is incorrect. The moment of inertia does depend on the shape of the object because it is influenced by how the mass is distributed relative to the axis of rotation.
- Different shapes (e.g., a solid cylinder vs. a hollow cylinder) will have different moments of inertia even if they have the same mass and radius.
- Therefore, Statement 2 is **false**.

### Conclusion
- **Statement 1** is true: \( I_1 < I_2 \) because the mass of the aluminum body is less than that of the iron body.
- **Statement 2** is false: The moment of inertia does depend on the shape of the object.

### Final Answer
The correct option is that Statement 1 is true and Statement 2 is false.