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Concepts Of Physics MCQ Edition [Volume 1]PhysicsFluid Mechanics

To assemble a barometer, a tube of length 1 m is completely filled with mercury and inverted in a mercury cup. On a certain day, the barometer reading is 76 cm . Suppose a 1 m tube is filled with mercury up to 76 cm and then sealed by a cork. It is inverted in a mercury cup and the cork is removed. The height of the mercury column in the tube above the surface in the cup will be

Options

  1. A> 76 cm
  2. B< 76 cm
  3. Czero
  4. D76 cm

Correct answer

B. < 76 cm

Step-by-step solution

Length of the tube is 100 cm . Initially, the tube contains 76 cm of mercury and 24 cm of air at atmospheric pressure, P₀ = 76 cm of Hg. When the tube is inverted in the mercury cup and the cork is removed, the air bubbles up and gets trapped at the closed top end. Let the new height of the mercury column be h . The length of the trapped air column becomes (100 - h) cm . The pressure of the trapped air is P = P₀ - h = 76 - h . Applying Boyle's law for the trapped air at constant temperature: P₀ V₁ = P V₂ 76 24A = (

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