QJEEAdv21Ph8c84: JEE Advanced 2021 Physics - Class 11 JEEAdv21Ph8c84 Solution: A soft plastic bottle, filled with water of density 1 gm/cc,…

A soft plastic bottle, filled with water of density 1 gm/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 5 gm, and it is made of a thick glass of density 2.5 gm/cc. Initially the bottle is sealed at atmosphere pressure p₀ = 10⁵ Pa so that the volume of the trapped air is v₀ = 3.3 cc. When the bottle is squeezed from outside at constant temperature, the pressure inside rises and the volume of the trapped air reduces. It is found that the test tube begins to sink at pressure p₀ + $$\mathrm{\Delta }$$p without changing its orientation. At this pressure, the volume of the trapped air is v₀ $$-$$ $$\mathrm{\Delta }$$v. Let $$\mathrm{\Delta }$$v = X cc and $$\mathrm{\Delta }$$p = Y $$\times$$ 10³ Pa.



The value of X is _______________.