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(Part 1) A soft plastic bottle, filled with water of density 1gm/cc, carries an inverted glass test-tube with some air (ideal gas) trapped as shown in the figure. The test-tube has a mass of 5gmm and it is made of a thick glass of density 2.5gm/cc. Initially the bottle is sealed at atmospheric pressure P0=10^5 Pa so that the volume of the trapped air is V0=3.3cc. When the bottle is squeezed from the outside at constant temperature, the pressure inside rises and the volume of trapped air reduces. It is found that the test-tube begins to sink at pressure P0+(delta)P without changing its orientation. At this pressure, the volume of the trapped air is V0-(delta)V. Let (delta)V=Xcc and (delta)P=Yx10^5Pa. The value of X=?

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