The gravitational force between two masses kept at a certain distance is p N. The same two masses are now kept in water and the distance between them is same. If the gravitational force between these two masses in water is q N, then

Options

A. `p=q`
B. `p lt q`
C. `p gt q`
D. None of these.

Answer

To solve the problem, we need to analyze the gravitational force between two masses in two different scenarios: when they are in air and when they are submerged in water. The gravitational force is given by Newton's law of gravitation, which states:

\[ F = \frac{G \cdot M_1 \cdot M_2}{r^2} \]

where:
- \( F \) is the gravitational force,
- \( G \) is the gravitational constant,
- \( M_1 \) and \( M_2 \) are the masses,
- \( r \) is the distance between the centers of the two masses.

### Step-by-Step Solution:

1. **Identify the gravitational force in air**:
- When the two masses are in air, the gravitational force is given as \( P \) N.
- According to the formula:
\[ P = \frac{G \cdot M_1 \cdot M_2}{r^2} \]

2. **Identify the gravitational force in water**:
- When the same two masses are placed in water, the distance \( r \) between them remains unchanged, and the masses \( M_1 \) and \( M_2 \) also remain unchanged.
- Therefore, the gravitational force in water is given as \( Q \) N, which can be expressed as:
\[ Q = \frac{G \cdot M_1 \cdot M_2}{r^2} \]

3. **Compare the two scenarios**:
- Since both equations for \( P \) and \( Q \) are identical, we can conclude:
\[ P = Q \]

4. **Conclusion**:
- The gravitational force between the two masses does not change when they are submerged in water. Thus, we find that:
\[ P = Q \]

### Final Answer:
The correct option is that \( P \) is equal to \( Q \).