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

Options

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

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 when they are submerged in a liquid of specific gravity 3.

### Step-by-Step Solution:

1. **Understanding Gravitational Force in Air**:
The gravitational force \( F \) between two masses \( m \) and \( M \) separated by a distance \( r \) in air is given by Newton's law of gravitation:
\[ F = \frac{G \cdot m \cdot M}{r^2} \]
where \( G \) is the universal gravitational constant.

2. **Effect of Medium on Gravitational Force**:
The gravitational force is derived from the masses and the distance between them. Importantly, it does not depend on the medium surrounding the masses. This means that whether the masses are in air, water, or any other medium, the gravitational force remains the same.

3. **Substituting the Medium**:
When the space around the masses is filled with a liquid of specific gravity 3, we need to recognize that specific gravity is a measure of density relative to water. However, this does not affect the gravitational force calculated by the formula above. The specific gravity indicates the buoyant force that may act on the masses, but it does not change the gravitational attraction between them.

4. **Conclusion**:
Therefore, the gravitational force between the two spheres when submerged in the liquid will still be:
\[ F' = \frac{G \cdot m \cdot M}{r^2} = F \]
Hence, the gravitational force remains \( F \).

### Final Answer:
The gravitational force will remain \( F \) even when the space around the masses is filled with a liquid of specific gravity 3.

---