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2014-10-10T13:25:43+05:30

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Yes, the bubble will rise in the water of the bottle.
The bubble rises due to buoyant force acting on it. The buoyant force acting on the bubble will be equal to the weight of the water displaced by the bubble. So the initial acceleration would be much higher than g as the mass of air bubble is negligible. (and it may attain terminal velocity)
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