Let `I_(A) and I_(B)` be moments of inertia of a body about two axes A and B respectively. The axis A passes through the centre of massof the body but B does not. Choose the correct option.

Options

A. `I_(A) lt I_(B)`
B. `I_(A) lt I_(B)`, whether the axes are parallel or not parallel
C. if the axes are parallel `I_(A) lt I_(B)`
D. If the axes are not parallel `I_(A) ge I_(B)`

Explanation

To solve the problem regarding the moments of inertia \( I_A \) and \( I_B \) of a body about two axes A and B, we will use the concept of the Parallel Axis Theorem.

### Step-by-Step Solution:

1. **Identify the Axes**:
- Axis A passes through the center of mass (CM) of the body.
- Axis B is parallel to axis A but does not pass through the center of mass.

2. **Recall the Parallel Axis Theorem**:
The Parallel Axis Theorem states that the moment of inertia about any axis (B) can be calculated using the moment of inertia about the center of mass (A) plus the product of the mass of the body (m) and the square of the distance (d) between the two axes:
\[ I_B = I_{CM} + m \cdot d^2 \]

3. **Substituting Values**:
Since axis A passes through the center of mass, we can denote:
\[ I_{CM} = I_A \]
Therefore, we can rewrite the equation for \( I_B \):
\[ I_B = I_A + m \cdot d^2 \]

4. **Analyze the Relationship**:
Since \( m \cdot d^2 \) is a positive quantity (as mass and distance squared are always positive), we can conclude that:
\[ I_B = I_A + m \cdot d^2 > I_A \]
This implies that:
\[ I_B > I_A \]

5. **Choose the Correct Option**:
Based on our analysis, the correct option is that the moment of inertia about axis B is greater than the moment of inertia about axis A:
- Thus, the correct statement is: \( I_B > I_A \).

### Conclusion:
The answer to the question is that the moment of inertia about axis B is greater than that about axis A, which corresponds to option three.