The gravitational attraction between the two bodies increases when their masses are

Options

A. reduced and distance is reduced
B. increased and distance is reduced
C. reduced and distance is increased
D. increased and distance is increased

Explanation

To solve the question regarding the gravitational attraction between two bodies and how it changes with their masses, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Gravitational Force**:
The gravitational force \( F \) between two bodies is given by Newton's law of gravitation:
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
where \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses of the two bodies, and \( r \) is the distance between their centers.

2. **Analyzing the Relationship**:
- The force \( F \) is **directly proportional** to the product of the masses \( m_1 \) and \( m_2 \). This means that if either mass increases, the gravitational force increases.
- The force \( F \) is **inversely proportional** to the square of the distance \( r \). This means that if the distance decreases, the gravitational force increases.

3. **Conditions for Increasing Gravitational Force**:
- To increase the gravitational attraction between the two bodies, we can either:
- **Increase the masses** \( m_1 \) and \( m_2 \).
- **Decrease the distance** \( r \) between the two bodies.

4. **Evaluating the Options**:
- **Option 1**: If the masses are reduced, the gravitational force will decrease.
- **Option 2**: If the masses are reduced and the distance is also reduced, the effect on force depends on how much each is changed. However, reducing the masses will generally lead to a decrease in force.
- **Option 3**: If the masses are reduced and the distance is increased, the gravitational force will definitely decrease.
- **Option 4**: If the masses are increased but the distance is also increased, the effect on force will depend on the relative changes. However, increasing the masses alone would increase the force.

5. **Conclusion**:
The gravitational attraction between the two bodies increases when their masses are **increased** and/or their distance is **decreased**. Therefore, the correct condition for increasing the gravitational attraction is to **increase the masses**.

### Final Answer:
The gravitational attraction between the two bodies increases when their masses are **increased**.