Choose the correct statements from the following

Options

A. The gravitational forces between two particles are an action and reaction pair.
B. Gravitational constant (`G`) is scalar but acceleration due to gravity (`g`) is a vector.
C. The values of `G` and `g` are to be determined experimentally.
D. `G` and `g` are constant everywhere.

Explanation

To solve the question, we need to analyze each of the given statements regarding gravitational forces and constants. Let's go through them one by one:

### Step-by-Step Solution:

1. **Statement 1: Gravitational forces between two particles are an action and reaction pair.**
- According to Newton's Third Law of Motion, for every action, there is an equal and opposite reaction. The gravitational force exerted by one particle on another is equal in magnitude and opposite in direction to the force exerted by the second particle on the first. Therefore, this statement is **true**.

2. **Statement 2: Gravitational constant \( G \) is a scalar but acceleration due to gravity \( g \) is a vector.**
- The gravitational constant \( G \) is indeed a scalar quantity as it represents a proportionality factor in the law of universal gravitation. On the other hand, the acceleration due to gravity \( g \) has both magnitude and direction (towards the center of the Earth), making it a vector quantity. Thus, this statement is **true**.

3. **Statement 3: The values of capital \( G \) and small \( g \) are to be determined experimentally.**
- The gravitational constant \( G \) is a universal constant that is determined experimentally. Similarly, the acceleration due to gravity \( g \) can vary based on location (e.g., altitude, depth) and is also determined experimentally. Therefore, this statement is **true**.

4. **Statement 4: Capital \( G \) and small \( g \) are constant everywhere.**
- This statement is **false**. While the gravitational constant \( G \) is indeed constant throughout the universe, the acceleration due to gravity \( g \) varies depending on factors such as altitude and geographical location. Therefore, this statement is incorrect.

### Conclusion:
The correct statements are:
- Statement 1: True
- Statement 2: True
- Statement 3: True
- Statement 4: False

Thus, the correct options are **1, 2, and 3**.