Two sphere of masses `m` and `M` are situated in air and the gravitational force between them is `F`. The space around the masses in now filled with a liquid of specific gravity `3`. The gravitational force will now be

Options

A. `(F)/(3)`
B. `(F)/(9)`
C. `3F`
D. `F`

Answer

To solve the problem, we need to analyze the gravitational force between two spheres of masses \( m \) and \( M \) when they are in air and then when the space around them is filled with a liquid of specific gravity \( 3 \).

### Step-by-Step Solution:

1. **Understanding Gravitational Force**:
The gravitational force \( F \) between two masses \( m \) and \( M \) separated by a distance \( r \) is given by the formula:
\[ F = \frac{G \cdot m \cdot M}{r^2} \]
where \( G \) is the gravitational constant.

2. **Effect of Medium**:
The problem states that the space around the masses is filled with a liquid of specific gravity \( 3 \). However, it is important to note that the gravitational force between two masses does not depend on the medium between them. The gravitational force is determined solely by the masses and the distance between them.

3. **Specific Gravity**:
The specific gravity of a liquid is a measure of its density relative to the density of water. A specific gravity of \( 3 \) means that the density of the liquid is \( 3 \) times that of water. However, this does not affect the gravitational attraction between the two masses.

4. **Conclusion**:
Since the gravitational force depends only on the masses \( m \) and \( M \) and the distance \( r \), and not on the medium (air or liquid), the gravitational force between the two spheres remains the same. Therefore, the gravitational force when the space is filled with the liquid will still be:
\[ F = \frac{G \cdot m \cdot M}{r^2} \]
Thus, the gravitational force will remain \( F \).

### Final Answer:
The gravitational force between the two spheres when the space is filled with a liquid of specific gravity \( 3 \) will still be \( F \).

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