The gravitational force between two particles of masses `m_1` and `m_2` seperated by certain distance in air medium is F. If they are taken to vaccum and seperated by the same distance, then the gravitational force between them will be

Options

A. greater than F
B. Less than F
C. F
D. Zero

Answer

To solve the problem, we need to understand the gravitational force between two masses and how it behaves in different mediums. The gravitational force \( F \) between two 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.

### Step-by-Step Solution:

1. **Identify the Given Information**:
- The gravitational force between two masses \( m_1 \) and \( m_2 \) in air is \( F \).
- The distance between the masses is \( r \).

2. **Understand the Gravitational Force Formula**:
- The formula for gravitational force \( F \) is independent of the medium in which the masses are located. It only depends on the masses and the distance between them.

3. **Consider the Scenario in Vacuum**:
- When the same two masses \( m_1 \) and \( m_2 \) are taken to a vacuum, the distance \( r \) remains the same.
- The formula for gravitational force still applies:
\[ F' = \frac{G m_1 m_2}{r^2} \]
where \( F' \) is the gravitational force in vacuum.

4. **Compare the Forces**:
- Since both scenarios (in air and in vacuum) use the same formula and the same values for \( m_1 \), \( m_2 \), and \( r \), we can conclude that:
\[ F' = F \]

5. **Final Conclusion**:
- Therefore, the gravitational force between the two masses when they are in vacuum and separated by the same distance is still \( F \).

### Final Answer:
The gravitational force between the two particles in vacuum will be \( F \).

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