STATEMENT - 1 Bernoulli's theorem is conversation of energy
because
STATEMENT - 2 Mass flowing per second at every cross section in tube of flow corresponding to incompressible liquid remains constant.

Options

A. Statement - 1 is True , Statement - 2 is True , Statement - 2 is a correct explanation for Statement - 2
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 analyze the statements provided in the question, we can break down the reasoning step by step.

### Step-by-Step Solution:

1. **Understanding Bernoulli's Theorem**:
Bernoulli's theorem states that for an incompressible, non-viscous fluid flowing in a streamline motion, the total mechanical energy along a streamline is constant. This can be expressed mathematically as:
\[ P + \frac{1}{2} \rho v^2 + \rho gh = \text{constant} \]
where \( P \) is the pressure, \( \rho \) is the fluid density, \( v \) is the fluid velocity, \( g \) is the acceleration due to gravity, and \( h \) is the height above a reference level.

**Hint**: Remember that Bernoulli's theorem relates pressure, kinetic energy per unit volume, and potential energy per unit volume.

2. **Conservation of Energy**:
The theorem can be interpreted as a statement of conservation of energy. The energy in the system is conserved as the fluid moves through different points in the flow. The work done by pressure forces results in changes in kinetic and potential energy.

**Hint**: Think about how energy transformations occur in fluid flow and how pressure contributes to this.

3. **Mass Flow Rate in Incompressible Fluids**:
For an incompressible fluid, the mass flow rate remains constant across any cross-section of the flow. This means that the mass of fluid entering a section must equal the mass of fluid exiting that section in a given time interval. Mathematically, this can be expressed as:
\[ A_1 v_1 = A_2 v_2 \]
where \( A \) is the cross-sectional area and \( v \) is the velocity of the fluid.

**Hint**: Consider the principle of continuity for incompressible fluids and how it applies to mass flow.

4. **Evaluating the Statements**:
- **Statement 1**: "Bernoulli's theorem is conservation of energy." This statement is true because Bernoulli's theorem indeed represents the conservation of mechanical energy in fluid flow.
- **Statement 2**: "Mass flowing per second at every cross-section in a tube of flow corresponding to incompressible liquid remains constant." This statement is also true as it reflects the principle of continuity for incompressible fluids.

5. **Conclusion**:
Both statements are true, but Statement 1 is a broader and more fundamental concept (conservation of energy) while Statement 2 is a specific condition that supports the application of Bernoulli's theorem. Therefore, Statement 1 is correct in the context of Bernoulli's theorem being a conservation principle.

**Final Answer**: Both statements are true, but Statement 1 is the correct explanation for Statement 2.