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Concepts Of Physics MCQ Edition [Volume 2]PhysicsKinetic Theory of Gases

As shown in the figure, a large closed cylindrical tank contains water. Initially, the air trapped above the water surface has a pressure of 2p₀ (where p₀ is the atmospheric pressure) and occupies a height h₀ . A hole is present in the wall of the tank at a depth h₁ below the top, allowing water to flow out. A long vertical tube, open to the atmosphere, is connected to the tank. Determine the initial height h₂ of the

Options

  1. Ap₀ g - h₁
  2. Bp₀ g + h₀
  3. C2p₀ g - h₀
  4. Dp₀ g - h₀

Correct answer

D. p₀ g - h₀

Step-by-step solution

Let us consider the pressure at the horizontal level of the water surface inside the tank. The pressure of the trapped air above the water surface in the tank is given as 2p₀ . Therefore, the pressure at the water surface inside the tank is 2p₀ . The water surface in the tank is at a depth h₀ below the top of the tank. The water level in the open vertical tube is at a height h₂ above the top of the tank. Thus, the total vertical depth of the water surface in the tank below the free surface in the open tube is h₂ +

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