Assertion: The velocity of flow of a liquid is smaller when pressure is larger and vice versa.
Reason: According to Bernoulli's theorem, for the stream line flow of an ideal liquid, the total energy per unit mass remains constant.

Options

A. Statement-1, is true, Statement-2 is true, Statement-2 is correct explanation for statement-1
B. Statement-1 is true, statement-2 is true, statement-2 is NOT a correct explantion 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, we need to analyze the assertion and reason provided and apply Bernoulli's theorem.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
The assertion states that "The velocity of flow of a liquid is smaller when pressure is larger and vice versa." This implies an inverse relationship between pressure and velocity in a fluid flow.

2. **Understanding the Reason**:
The reason states that "According to Bernoulli's theorem, for the streamline flow of an ideal liquid, the total energy per unit mass remains constant." Bernoulli's theorem can be expressed as:
\[ P + \frac{1}{2} \rho V^2 + \rho g h = \text{constant} \]
where \( P \) is the pressure, \( \rho \) is the density of the fluid, \( V \) is the velocity, and \( h \) is the height above a reference level.

3. **Applying Bernoulli's Theorem**:
For a horizontal pipe, the height \( h \) remains constant, so we can simplify Bernoulli's equation to:
\[ P_1 + \frac{1}{2} \rho V_1^2 = P_2 + \frac{1}{2} \rho V_2^2 \]
Rearranging gives:
\[ P_2 = P_1 + \frac{1}{2} \rho (V_1^2 - V_2^2) \]

4. **Analyzing the Relationship**:
If we assume \( V_1 < V_2 \) (the velocity at point 1 is less than at point 2), then \( V_1^2 < V_2^2 \). This means that \( V_1^2 - V_2^2 \) is negative, leading to:
\[ P_2 < P_1 \]
This indicates that when the velocity increases (from \( V_1 \) to \( V_2 \)), the pressure decreases (from \( P_1 \) to \( P_2 \)), confirming the assertion.

5. **Conclusion**:
Both the assertion and the reason are true. The assertion correctly describes the relationship between pressure and velocity in fluid flow, and the reason accurately reflects Bernoulli's theorem.

### Final Answer:
Both the assertion and the reason are true, and the correct option is that both statements are valid.

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