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 given statements and arrive at a conclusion, let's break down the problem step by step.

### Step 1: Understanding Moment of Inertia
The moment of inertia (I) of an object is a measure of how difficult it is to change its rotational motion about a particular axis. It depends on both the mass of the object and how that mass is distributed relative to the axis of rotation.

### Step 2: Analyzing Statement 1
Statement 1 claims that the moment of inertia of two bodies with identical geometrical shapes, one made of aluminum (I1) and the other made of iron (I2), satisfies the inequality I1 < I2.

- **Reasoning**:
- Aluminum has a lower density than iron.
- Since both objects have the same shape and size, the mass of the aluminum object will be less than that of the iron object.
- Therefore, the moment of inertia, which is dependent on mass, will also be less for the aluminum object.

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

- **Reasoning**:
- 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 with respect to the axis of rotation.
- For example, if the mass is distributed further from the axis, the moment of inertia increases, and if it is closer, the moment of inertia decreases.

### Step 4: Conclusion
Based on the analysis:
- **Statement 1** is true: I1 < I2 because aluminum has a lower density than iron.
- **Statement 2** is false: Moment of inertia does depend on the shape of the object.

Thus, the correct conclusion is that Statement 1 is true and Statement 2 is false.

### Final Answer
- **Correct Option**: Statement 1 is true, Statement 2 is false.

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