Pressure in bottle - Finding depth

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To determine how far a bottle must be submerged for 100 cubic centimeters of water to enter, the pressure inside the bottle must equal the hydrostatic pressure outside at the bottle's opening. The hydrostatic pressure can be calculated using the formula P = ρgh, where ρ is the water density, g is the acceleration due to gravity, and h is the depth. Applying Boyle's law, the change in air pressure inside the bottle as water enters must also be considered. The discussion emphasizes the need to equate the pressures and solve for the depth required to achieve this condition. Understanding these principles is crucial for solving the problem accurately.
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Homework Statement



A bottle, full of air at atmospheric pressure, whose volume is 500 cubic centimeters, is sunken mouth downwards below the surface of a pond. How far must it be sunk for 100 cubic centimeters of water to run up into the bottle?

Homework Equations





The Attempt at a Solution


The only things i know are that the pressure at the level of the bottle opening must be the same inside and outside. But I'm not sure how to find the depth needed.
 
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I hope the attached picture helps. Determine the pressure outside and inside of the bottle at the level of opening. Apply the formula for hydrostatic pressure of water and Boyle's law to get the air pressure inside the bottle.

ehild
 
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