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 the assertion (A) and the reason (R) separately.

### Step 1: Understanding the Assertion (A)
The assertion states that "Work done by the gravitational force is positive when the two point masses are brought from infinity to any two points in space."

- When two point masses are at infinity, the gravitational force between them is negligible (effectively zero). As we bring them closer together, the gravitational force acts as an attractive force.
- The work done by the gravitational force can be calculated using the formula:
\[ W = F \cdot d \cdot \cos(\theta) \]
where \(F\) is the gravitational force, \(d\) is the displacement, and \(\theta\) is the angle between the force and the displacement vector.
- Since the gravitational force is attractive and the masses are moving towards each other, the angle \(\theta\) is 0 degrees, making \(\cos(0) = 1\). Therefore, the work done is positive.

### Step 2: Understanding the Reason (R)
The reason states that "Gravitational potential energy increases during the above process."

- Gravitational potential energy (U) is defined as:
\[ U = -\frac{G m_1 m_2}{r} \]
where \(G\) is the gravitational constant, \(m_1\) and \(m_2\) are the masses, and \(r\) is the distance between them.
- At infinity, the potential energy is zero. As the masses are brought closer together, \(r\) decreases, causing \(U\) to become more negative (i.e., it decreases).
- Therefore, the gravitational potential energy does not increase; it actually decreases as the masses approach each other.

### Conclusion
- The assertion (A) is true: Work done by the gravitational force is positive.
- The reason (R) is false: Gravitational potential energy does not increase; it decreases.

Thus, the correct answer is that the assertion is true, but the reason is false.

### Final Answer
Assertion (A) is true, Reason (R) is false.

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