The force of gravitation between two bodies can be zero if the separation between the bodies becomes

Options

A. 1
B. 0
C. `-1`
D. infinity

Answer

To solve the question regarding when the force of gravitation between two bodies can be zero, we will follow these steps:

### Step-by-Step Solution:

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

2. **Analyzing the Force Equation**:
From the equation, we see that the gravitational force \( F \) is inversely proportional to the square of the distance \( R \). This means that as \( R \) increases, \( F \) decreases.

3. **Condition for Zero Force**:
To find when the gravitational force \( F \) becomes zero, we need to consider the behavior of the equation as \( R \) changes. The force can only be zero if the denominator \( R^2 \) approaches infinity.

4. **Setting \( R \) to Infinity**:
If we let \( R \) approach infinity, we can substitute it into our equation:
\[ F = \frac{G m_1 m_2}{R^2} \quad \text{(as \( R \to \infty \))} \]
This leads to:
\[ F = \frac{G m_1 m_2}{\infty} = 0 \]
Thus, the gravitational force becomes zero when the separation \( R \) between the two bodies is infinite.

5. **Conclusion**:
Therefore, the gravitational force between two bodies can be zero if the separation between the bodies becomes infinite.

### Final Answer:
The force of gravitation between two bodies can be zero if the separation between the bodies becomes infinite.

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