A : Work done by the gravitational force is positive when the two point masses are brought from infinity to any two points in space .
R : Gravitational potential energy increases during the above process .

Options

A. If both Assertion & Reason are true . And the reason is the correct explanation of the assertion , then mark (1)
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion , then mark (2)
C. If Assertion is true statement but Reason is false , then mark (3)
D. If both Assertion and Reason are false statement , then mark (4)

Answer

To solve the question, we need to analyze both the Assertion (A) and the Reason (R) provided.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that the work done by the gravitational force is positive when two point masses are brought from infinity to any two points in space.
- When two masses are brought from infinity (where gravitational potential energy is considered zero) to a point in space, the gravitational force does work on the masses.

2. **Calculating Work Done by Gravitational Force**:
- The work done \( W \) by the gravitational force can be expressed as:
\[ W = U_{\text{initial}} - U_{\text{final}} \]
- At infinity, the gravitational potential energy \( U_{\text{initial}} = 0 \).
- When the masses are at a distance \( r \), the gravitational potential energy \( U_{\text{final}} \) is given by:
\[ U_{\text{final}} = -\frac{G m_1 m_2}{r} \]
- Therefore, the work done by the gravitational force becomes:
\[ W = 0 - \left(-\frac{G m_1 m_2}{r}\right) = \frac{G m_1 m_2}{r} \]
- Since \( G, m_1, m_2, \) and \( r \) are all positive quantities, \( W \) is positive.

3. **Understanding the Reason (R)**:
- The reason states that gravitational potential energy increases during the process.
- However, as we have established, when moving from infinity to a point in space, the potential energy decreases from zero to a negative value.
- Thus, the statement that gravitational potential energy increases is incorrect.

4. **Conclusion**:
- The assertion (A) is correct because the work done by the gravitational force is indeed positive.
- The reason (R) is incorrect because the gravitational potential energy decreases, not increases.

### Final Answer:
- The assertion is correct, but the reason is incorrect. Therefore, the correct option is that Assertion (A) is true and Reason (R) is false.

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