Statement-1: The stream of water emerging from a wate tap "necks down" as it falls.
Statement-2: The volume flow rate at different levels is same.

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 problem, we need to analyze the two statements given:

**Statement-1:** The stream of water emerging from a water tap "necks down" as it falls.
**Statement-2:** The volume flow rate at different levels is the same.

### Step-by-Step Solution:

1. **Understanding Volume Flow Rate:**
The volume flow rate (Q) is defined as the volume of fluid that passes through a given surface per unit time. It can be expressed as:
\[ Q = A \cdot v \]
where \(A\) is the cross-sectional area and \(v\) is the velocity of the fluid.

2. **Applying the Continuity Equation:**
For an incompressible fluid (like water), the volume flow rate must remain constant along the stream. Therefore, at two points (1 and 2) in the stream:
\[ Q_1 = Q_2 \implies A_1 \cdot v_1 = A_2 \cdot v_2 \]
where \(A_1\) and \(v_1\) are the area and velocity at point 1, and \(A_2\) and \(v_2\) are the area and velocity at point 2.

3. **Considering the Effect of Gravity:**
As the water falls, it accelerates due to gravity. This means that the velocity of the water increases as it falls:
\[ v_2 > v_1 \]
Since the volume flow rate must remain constant, if \(v_2\) increases, then \(A_2\) must decrease to keep the product \(A \cdot v\) constant.

4. **Conclusion on Areas:**
From the equation \(A_1 \cdot v_1 = A_2 \cdot v_2\), if \(v_2 > v_1\), it follows that:
\[ A_2 < A_1 \]
This indicates that the cross-sectional area of the stream of water decreases (or "necks down") as it falls.

5. **Final Evaluation of Statements:**
- **Statement-1** is true: The stream of water does neck down as it falls.
- **Statement-2** is also true: The volume flow rate at different levels is indeed the same, as derived from the continuity equation.

Thus, we conclude that both statements are true, and Statement-2 correctly explains Statement-1.

### Final Answer:
Both statements are true, and Statement-2 is the correct explanation of Statement-1.

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