STATEMENT - 1 When a body is inside a static liquid it experience is up by buoyancy force because
STATEMENT - 2 : Pressure varies with depth in a static liquid .

Options

A. Statement - 1 is True , Statement - 2 is True , Statement - 2 is a correct explanation for Statement - 1
B. Statement -1 is True , Statement - 2 is True , Statement - 2 is Not a correct explanation for Statement - 1 .
C. Statement - 1 is True , Statement - 2 is False
D. Statement - 1 is False , Statement - 2 is True

Answer

To solve the question regarding the buoyant force experienced by a body submerged in a static liquid and its relation to pressure variation with depth, we can break down the explanation into clear steps.

### Step-by-Step Solution:

1. **Understanding Buoyant Force**:
- When a body is submerged in a fluid, it experiences an upward force known as buoyant force. This force is due to the difference in pressure acting on the top and bottom surfaces of the submerged body.

2. **Pressure Variation with Depth**:
- In a static liquid, pressure increases with depth. This can be expressed by the equation:
\[ P = \rho g h \]
where \( P \) is the pressure, \( \rho \) is the density of the liquid, \( g \) is the acceleration due to gravity, and \( h \) is the depth from the surface of the liquid.

3. **Analyzing the Forces**:
- Consider a cylindrical body submerged in the liquid. Let the height of the cylinder be \( H \). The pressure at the bottom of the cylinder (depth \( h_2 \)) will be greater than the pressure at the top of the cylinder (depth \( h_1 \)).
- The pressure at the top of the cylinder is given by:
\[ P_{top} = \rho g h_1 \]
- The pressure at the bottom of the cylinder is given by:
\[ P_{bottom} = \rho g h_2 \]
- Since \( h_2 > h_1 \), it follows that \( P_{bottom} > P_{top} \).

4. **Calculating the Buoyant Force**:
- The buoyant force \( F_b \) can be calculated as the difference in force due to pressure on the bottom and top surfaces of the cylinder:
\[ F_b = A \cdot (P_{bottom} - P_{top}) \]
where \( A \) is the cross-sectional area of the cylinder.
- Substituting the pressures:
\[ F_b = A \cdot (\rho g h_2 - \rho g h_1) = A \cdot \rho g (h_2 - h_1) \]
- This shows that the buoyant force is directed upwards, confirming that the body experiences an upward force when submerged.

5. **Conclusion**:
- Therefore, Statement 1 is correct: a body submerged in a static liquid experiences an upward buoyant force.
- Statement 2 is also correct: pressure varies with depth in a static liquid, which explains why the buoyant force acts upwards.

### Final Statement:
Both statements are true, and Statement 2 provides a correct explanation for Statement 1.

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