If the distance between two given bodies is halved, then the force of attraction between them

Options

A. is halved
B. is quadrupled.
C. becomes twice.
D. remains constant.

Explanation

To solve the question of how the force of attraction between two bodies changes when the distance between them is halved, we can use Newton's Law of Universal Gravitation. According to this law, the gravitational force \( F \) between two masses \( m_1 \) and \( m_2 \) separated by a distance \( r \) is given by the formula:

\[ F = G \frac{m_1 m_2}{r^2} \]

where \( G \) is the gravitational constant.

### Step-by-Step Solution:

1. **Understand the Formula**: The gravitational force is inversely proportional to the square of the distance between the two bodies. This means that if the distance \( r \) decreases, the force \( F \) increases.

2. **Initial Force Calculation**: Let’s denote the initial distance between the two bodies as \( r \). The initial force of attraction can be expressed as:
\[ F_1 = G \frac{m_1 m_2}{r^2} \]

3. **Halving the Distance**: If the distance is halved, the new distance \( r' \) becomes:
\[ r' = \frac{r}{2} \]

4. **New Force Calculation**: Now, we can calculate the new force of attraction \( F_2 \) when the distance is halved:
\[ F_2 = G \frac{m_1 m_2}{(r')^2} = G \frac{m_1 m_2}{\left(\frac{r}{2}\right)^2} \]

5. **Simplifying the New Force**: When we simplify \( F_2 \):
\[ F_2 = G \frac{m_1 m_2}{\left(\frac{r^2}{4}\right)} = G \frac{m_1 m_2 \cdot 4}{r^2} = 4 \left(G \frac{m_1 m_2}{r^2}\right) \]

6. **Conclusion**: Thus, the new force of attraction \( F_2 \) is four times the initial force \( F_1 \):
\[ F_2 = 4F_1 \]

### Final Answer:
If the distance between two given bodies is halved, then the force of attraction between them becomes four times greater.