Find the force exerted by the water on a `2m^2` plane surface of a large stone placed at the bottom of a sea 500 m deep. Does the force depend on the orientation of the surface? Neglect the size of the stone in comparison to the depth of the sea.

Explanation

To find the force exerted by the water on a 2 m² plane surface of a large stone placed at the bottom of a sea 500 m deep, we can follow these steps:

### Step 1: Understand the Problem
We need to calculate the force exerted by water on a surface at a certain depth. We are given:
- Depth of water (h) = 500 m
- Area of the surface (A) = 2 m²
- Density of water (ρ) = 1000 kg/m³ (standard value)
- Acceleration due to gravity (g) = 10 m/s² (approximate value)

### Step 2: Calculate the Pressure at Depth
The pressure (P) at a depth in a fluid is given by the formula:
\[ P = \rho g h \]
Substituting the values:
\[ P = 1000 \, \text{kg/m}^3 \times 10 \, \text{m/s}^2 \times 500 \, \text{m} \]

### Step 3: Perform the Calculation
Calculating the pressure:
\[ P = 1000 \times 10 \times 500 \]
\[ P = 5000000 \, \text{Pa} \, \text{(Pascals)} \]

### Step 4: Calculate the Force
The force (F) exerted by the water on the surface can be calculated using the formula:
\[ F = P \times A \]
Substituting the values:
\[ F = 5000000 \, \text{Pa} \times 2 \, \text{m}^2 \]

### Step 5: Perform the Calculation
Calculating the force:
\[ F = 5000000 \times 2 \]
\[ F = 10000000 \, \text{N} \]

### Conclusion
The force exerted by the water on the 2 m² surface of the stone is \( 10^7 \, \text{N} \).

### Step 6: Orientation of the Surface
Regarding whether the force depends on the orientation of the surface, we note that pressure at a point in a fluid is the same in all directions. Therefore, the force exerted on the surface does not depend on its orientation, as long as the size of the stone is neglected in comparison to the depth of the sea.

### Final Answer
- The force exerted by the water on the surface is \( 10^7 \, \text{N} \).
- The force does not depend on the orientation of the surface.