A body brought into the sea from the surface. Which of the following graphs represents correctly the variation of the pressure P on the body with increase in the depth d? [1 atmospheric pressure `~~ 10^(5) Nm^(-2)`]

Options

A.
B.
C.
D.

Explanation

To solve the question regarding the variation of pressure \( P \) on a body with an increase in depth \( d \) in the sea, we can follow these steps:

### Step 1: Understand the relationship between pressure and depth
The pressure \( P \) at a certain depth \( d \) in a fluid is given by the formula:

\[ P = P_0 + \rho g d \]

where:
- \( P_0 \) is the atmospheric pressure at the surface (approximately \( 10^5 \, \text{N/m}^2 \)),
- \( \rho \) is the density of the fluid (for water, approximately \( 1000 \, \text{kg/m}^3 \)),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)),
- \( d \) is the depth below the surface.

### Step 2: Identify the initial pressure at the surface
At the surface of the sea (where \( d = 0 \)), the pressure \( P \) is equal to the atmospheric pressure \( P_0 \). Therefore, when \( d = 0 \):

\[ P = P_0 \approx 10^5 \, \text{N/m}^2 \]

### Step 3: Analyze how pressure changes with depth
As the depth \( d \) increases, the term \( \rho g d \) increases linearly with \( d \). This means that the pressure \( P \) increases linearly as well.

### Step 4: Sketch the graph
- On the Y-axis, we plot the pressure \( P \).
- On the X-axis, we plot the depth \( d \).
- At \( d = 0 \), \( P = P_0 \).
- As \( d \) increases, \( P \) increases linearly due to the linear relationship established by the formula.

### Step 5: Determine the shape of the graph
The graph will start at \( P_0 \) when \( d = 0 \) and will rise linearly as \( d \) increases. This indicates that the graph is a straight line with a positive slope.

### Conclusion
The correct graph representing the variation of pressure \( P \) with an increase in depth \( d \) is a straight line starting from \( P_0 \) at \( d = 0 \) and increasing linearly.

### Final Answer
The correct option is the one that shows a linear increase in pressure starting from atmospheric pressure as depth increases.

---