Statement-1 : When an air bubble moves up from the bottom of a lake, its acceleration decreases and becomes zero.
And
Statement-2 : When an air bubble moves up from the bottom of a lake, its velocity increases and become constant.

Options

A. a.Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1
B. b.Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1
C. c.Statement-1 is True, Statement-2 is False
D. d.Statement-1 is False, Statement-2 is True

Answer

To analyze the given statements regarding the motion of an air bubble rising in a lake, we will break down the problem step by step.

### Step 1: Understand the Forces Acting on the Air Bubble
When an air bubble rises in a fluid (like water in a lake), two main forces act on it:
- **Buoyant Force (B)**: This force acts upwards and is given by Archimedes' principle. It is equal to the weight of the fluid displaced by the bubble.
- **Viscous Force (Fv)**: This force acts downwards due to the viscosity of the fluid. It is proportional to the velocity of the bubble and can be expressed as \( F_v = 6 \pi \eta r v \), where \( \eta \) is the viscosity of the fluid, \( r \) is the radius of the bubble, and \( v \) is the velocity of the bubble.

### Step 2: Analyze the Motion of the Bubble
Initially, when the bubble starts to rise, the buoyant force is greater than the viscous force. This results in a net upward force, causing the bubble to accelerate upwards.

### Step 3: Determine the Change in Acceleration
As the bubble continues to rise, its velocity increases. Since the viscous force is proportional to the velocity, as the velocity increases, the viscous force also increases. Eventually, the viscous force will equal the buoyant force, leading to a net force of zero.

### Step 4: Conclusion on Acceleration
When the net force becomes zero, the acceleration of the bubble becomes zero. Therefore, the first statement is correct: "When an air bubble moves up from the bottom of a lake, its acceleration decreases and becomes zero."

### Step 5: Analyze the Velocity of the Bubble
As the bubble rises and its acceleration decreases to zero, it reaches a point where it moves with constant velocity. This means that the second statement is also correct: "When an air bubble moves up from the bottom of a lake, its velocity increases and becomes constant."

### Step 6: Determine the Relationship Between the Statements
While both statements are true, the second statement does not serve as a correct explanation for the first statement. The first statement describes the change in acceleration, while the second statement describes the change in velocity. Thus, the first statement is not dependent on the second statement for its validity.

### Final Conclusion
- **Statement 1**: True
- **Statement 2**: True
- **Explanation Relationship**: Statement 2 is not the correct explanation of Statement 1.

### Answer
The correct option is B: Statement 1 is true, Statement 2 is true, but Statement 2 is not the correct explanation of Statement 1.

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