Assertion : Moment of inertia about an axis passing throught centre of mass is always minimum
Reason : Theorem of parallel axis can be applied for 2-D as well as 3-D bodies.

Options

A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion
C. If Assertion is true but Reason is fasle
D. If Assertion is false but Reason is true

Explanation

To solve the question, we need to analyze the assertion and reason provided:

**Assertion:** Moment of inertia about an axis passing through the center of mass is always minimum.
**Reason:** Theorem of parallel axis can be applied for 2-D as well as 3-D bodies.

### Step-by-step Solution:

1. **Understanding Moment of Inertia:**
- The moment of inertia (I) of a body about an axis is a measure of how difficult it is to change its rotational motion about that axis. It depends on the mass distribution relative to the axis of rotation.

2. **Moment of Inertia at Center of Mass:**
- For any rigid body, the moment of inertia about an axis passing through its center of mass is always the minimum compared to any other parallel axis. This is because any shift of the axis away from the center of mass increases the moment of inertia by an amount proportional to the square of the distance from the center of mass.

3. **Applying the Parallel Axis Theorem:**
- The parallel axis theorem states that if you know the moment of inertia about an axis through the center of mass (I_cm), you can find the moment of inertia about any parallel axis a distance d away using the formula:
\[ I = I_{cm} + md^2 \]
- Here, m is the mass of the body and d is the distance between the two axes.

4. **Example with Different Bodies:**
- Consider a ring and a solid sphere:
- For a ring of mass \( m \) and radius \( r \), the moment of inertia about its center of mass is:
\[ I_{cm} = \frac{1}{2} m r^2 \]
- For a solid sphere of mass \( M \) and radius \( R \), the moment of inertia about its center of mass is:
\[ I_{cm} = \frac{2}{5} M R^2 \]

5. **Conclusion on the Assertion:**
- Since the moment of inertia about the center of mass is always the minimum, the assertion is true.

6. **Conclusion on the Reason:**
- The reason states that the parallel axis theorem can be applied to both 2-D and 3-D bodies, which is also true. However, it does not explain why the moment of inertia at the center of mass is minimum.

7. **Final Evaluation:**
- Both the assertion and reason are true, but the reason does not correctly explain the assertion. Therefore, the correct conclusion is that the assertion is true, and the reason is true but not a correct explanation.

### Final Answer:
- The assertion is true, and the reason is true but does not explain the assertion. Thus, the answer is option B.