When two bodies are saparated by certain distance the gravitational force between then is F. If distance is increased by 100%,then gravitational force becomes --

Options

A. `F/4`
B. 4F
C. `F/2`
D. 2F

Answer

To solve the problem, we will use Newton's law of gravitation, which states that the gravitational force \( F \) between two masses \( m_1 \) and \( m_2 \) separated by a distance \( R \) is given by the formula:

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

where \( G \) is the universal gravitational constant.

### Step-by-Step Solution:

1. **Identify the initial gravitational force**:
The initial gravitational force between the two bodies is given as \( F \). This can be expressed as:
\[ F = \frac{G m_1 m_2}{R^2} \]

2. **Understand the change in distance**:
The problem states that the distance between the two bodies is increased by 100%. If the original distance is \( R \), then increasing it by 100% means the new distance \( R' \) is:
\[ R' = R + 100\% \text{ of } R = R + R = 2R \]

3. **Calculate the new gravitational force**:
Now, we need to find the new gravitational force \( F' \) when the distance is \( R' = 2R \):
\[ F' = \frac{G m_1 m_2}{(2R)^2} \]
Simplifying this, we get:
\[ F' = \frac{G m_1 m_2}{4R^2} \]

4. **Relate the new force to the original force**:
We can express \( F' \) in terms of \( F \):
\[ F' = \frac{1}{4} \cdot \frac{G m_1 m_2}{R^2} = \frac{1}{4} F \]

5. **Conclusion**:
Therefore, when the distance is increased by 100%, the new gravitational force becomes:
\[ F' = \frac{F}{4} \]

### Final Answer:
The gravitational force becomes \( \frac{F}{4} \).