STATEMENT - 1 : A body has no inertia, when it is at the centre of the earth.
and
STATEMENT - 2 : At centre of the earth the mass of a body is non - zero .

Options

A. Statement -1 True, Statement -2 is True , Statement - 2 is a 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, we need to understand the concepts of inertia and mass in the context of a body located at the center of the Earth.

### Step-by-Step Solution:

1. **Understanding Inertia**:
- Inertia is the property of a body to resist changes in its state of motion. It is directly related to the mass of the body. The greater the mass, the greater the inertia.

2. **Statement 1 Analysis**:
- The first statement claims that a body has no inertia when it is at the center of the Earth.
- At the center of the Earth, the gravitational force acting on the body is zero because the gravitational pull from all sides cancels out. Therefore, the weight (W = mg) of the body is zero.
- However, the mass of the body (m) is not zero. Mass is a measure of the amount of matter in the body and does not change regardless of location. Therefore, even though the weight is zero, the mass (and thus the inertia) is still present.

3. **Conclusion for Statement 1**:
- Since the mass is non-zero, the body does have inertia. Thus, Statement 1 is **false**.

4. **Statement 2 Analysis**:
- The second statement asserts that at the center of the Earth, the mass of a body is non-zero.
- This is true because mass is an intrinsic property of matter and does not change based on location. Regardless of where the body is, its mass remains the same.

5. **Conclusion for Statement 2**:
- Therefore, Statement 2 is **true**.

6. **Final Evaluation**:
- Based on the analysis, we conclude that:
- Statement 1 is false.
- Statement 2 is true.
- The correct option is D: Statement 1 is false and Statement 2 is true.

### Summary:
- **Statement 1**: False (A body has inertia regardless of its position, as long as it has mass).
- **Statement 2**: True (Mass is a non-zero quantity for any body).