Assertion: The centre of gravity of a body coincides with its centre of mass only if the gravitational field does not vary form one part of the body to the other.
Reason: Centre of gravity is independent of the gravitational field.

Options

A. If both assertion and reason are true 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 false.
D. If both assertion and reason are false.

Explanation

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

### Step 1: Understand the Assertion
The assertion states that "The centre of gravity of a body coincides with its centre of mass only if the gravitational field does not vary from one part of the body to the other."

- **Explanation**: The centre of gravity is the point where the total weight of the body can be considered to act. When the gravitational field is uniform (i.e., it does not vary across the body), the centre of gravity and the centre of mass will coincide. If the gravitational field varies, the centre of gravity will shift away from the centre of mass.

### Step 2: Understand the Reason
The reason states that "Centre of gravity is independent of the gravitational field."

- **Explanation**: This statement is incorrect. The centre of gravity is dependent on the gravitational field because it is defined based on the distribution of weight in a gravitational field. If the gravitational field changes, the centre of gravity will also change.

### Step 3: Conclusion
- The assertion is **true** because the centre of gravity coincides with the centre of mass only in a uniform gravitational field.
- The reason is **false** because the centre of gravity is indeed dependent on the gravitational field.

### Final Answer
Based on the analysis:
- The correct option is **C**: Assertion is true, but the reason is false.

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