STATEMENT-1: The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up, but tends to narrow down when held vertically down.
STATEMENT-2: In any steady flow of an incompressible fluid, the volume flow rate of the fluid remains constant.

Options

A. If both assertion and reason are true and the reason is correct explanation of the assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true, but the reason is false.
D. If assertion is false, but the reason is true.

Explanation

To analyze the statements provided in the question, we will break down the reasoning step by step.

### Step 1: Understanding Statement 1
Statement 1 describes the behavior of water flowing from a garden hosepipe when held in two different orientations: vertically up and vertically down.

- **When held vertically up**: The stream of water spreads out like a fountain. This occurs because the water is moving against gravity, and as it exits the hosepipe, the kinetic energy of the water is converted into potential energy, causing the water to spread out.

- **When held vertically down**: The stream of water narrows down. In this case, the water is moving with gravity, and the acceleration due to gravity increases the speed of the water as it exits the hosepipe.

### Step 2: Understanding Statement 2
Statement 2 states that in any steady flow of an incompressible fluid, the volume flow rate remains constant.

- The volume flow rate (Q) is defined as the product of the cross-sectional area (A) of the flow and the velocity (V) of the fluid:
\[ Q = A \times V \]
- For an incompressible fluid, the volume flow rate must remain constant throughout the flow. This means that if the area decreases, the velocity must increase to keep the product \( A \times V \) constant.

### Step 3: Applying the Continuity Equation
When the hosepipe is held down:

- The cross-sectional area (A) of the stream decreases as the water flows downward.
- According to the continuity equation, if the area decreases, the velocity (V) of the water must increase to maintain a constant flow rate.

### Step 4: Conclusion
Based on the analysis:

- **Statement 1** is true because it accurately describes the behavior of the water stream in both orientations.
- **Statement 2** is also true as it correctly explains the principle of conservation of mass for incompressible fluids.

Furthermore, Statement 2 serves as the correct explanation for Statement 1, as it provides the underlying principle (continuity equation) that explains why the stream behaves differently when oriented in different directions.

### Final Answer
Both statements are true, and Statement 2 is the correct explanation of Statement 1. Thus, the correct answer is option 1.

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