Assertion : At the centre of earth, a body has centre of mass , but no centre of gravity.
Reason : This is because `g = 0` at the centre of earth.

Options

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

Explanation

To solve the question regarding the assertion and reason, we need to analyze both statements carefully.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that at the center of the Earth, a body has a center of mass but no center of gravity.
- The center of mass is a point representing the average position of the mass of an object. It is a property of the object itself and does not depend on external factors like gravity.

2. **Understanding the Reason**:
- The reason given is that the gravitational acceleration (g) is zero at the center of the Earth.
- Gravitational acceleration is the force per unit mass experienced by an object due to gravity. At the center of the Earth, the gravitational forces from all surrounding mass cancel out, resulting in zero net gravitational force.

3. **Analyzing the Assertion**:
- At the center of the Earth, although a body has mass and thus a center of mass, the gravitational force acting on it is zero.
- Therefore, the concept of a center of gravity, which is the point where the gravitational force can be considered to act, becomes meaningless when there is no gravitational force.

4. **Analyzing the Reason**:
- The reason correctly explains why the assertion is true. Since gravitational acceleration is zero at the center of the Earth, there is no gravitational force acting on the body, confirming that there is no center of gravity.

5. **Conclusion**:
- Both the assertion and the reason are true, and the reason provides a valid explanation for the assertion.

### Final Answer:
- **Assertion**: True
- **Reason**: True
- The reason explains the assertion.