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An air bubble rises from the bottom of a...

An air bubble rises from the bottom of a lake of large depth. The rising speed of air bubble will

A

go on increasing till it reaches surface

B

go on decreasing till it reaches surface

C

increases in two beginning, then will become constant

D

be constant all throughout.

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The correct Answer is:
To solve the problem of how the rising speed of an air bubble changes as it rises from the bottom of a lake of large depth, we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Forces Acting on the Bubble**: - When the air bubble rises, it experiences three main forces: - The buoyant force acting upwards (due to the displaced water). - The weight of the bubble acting downwards (due to the air inside). - The drag force acting opposite to the direction of motion (due to the water resistance). 2. **Apply Archimedes' Principle**: - According to Archimedes' principle, the buoyant force on the bubble is equal to the weight of the water displaced by the bubble. This force is greater than the weight of the bubble when it first starts to rise. 3. **Consider the Initial Rising Phase**: - Initially, when the bubble starts to rise, the buoyant force is greater than the weight of the bubble. This results in an upward acceleration, causing the bubble to speed up. 4. **Account for Increasing Drag Force**: - As the bubble rises, its speed increases, which in turn increases the drag force acting against it. The drag force is proportional to the square of the velocity of the bubble. 5. **Reach Terminal Velocity**: - Eventually, the bubble will reach a point where the buoyant force equals the sum of the weight of the bubble and the drag force. At this point, the net force acting on the bubble becomes zero, and the bubble stops accelerating. It then moves at a constant speed known as terminal velocity. 6. **Conclusion**: - Therefore, the rising speed of the air bubble will initially increase as it rises, and then it will become constant once terminal velocity is reached. ### Final Answer: The rising speed of the air bubble will initially increase and then become constant.
To solve the problem of how the rising speed of an air bubble changes as it rises from the bottom of a lake of large depth, we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Forces Acting on the Bubble**: - When the air bubble rises, it experiences three main forces: - The buoyant force acting upwards (due to the displaced water). - The weight of the bubble acting downwards (due to the air inside). ...
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