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Paragraph: P_ 14-16 : Paragraph for Questions Nos. 14 to 16 A fixed thermally conducting cylinder has a radius R and height L₀ . The cylinder is open at its bottom and has a small hole at its top. A piston of mass M is held at a distance L from the top surface as shown in the figure. The atmospheric pressure is p₀ . Question: The piston is taken completely out of the cylinder. The hole at the top is sealed. A water t

Options

  1. Ag (L₀-H )^2+p₀ (L₀-H )+L₀ p₀=0
  2. Bg (L₀-H )^2-p₀ (L₀-H )-L₀ p₀=0
  3. Cg (L₀-H )^2+p₀ (L₀-H )-L₀ p₀=0
  4. Dg (L₀-H )^2-p₀ (L₀-H )+L₀ p₀=0

Correct answer

C. g (L₀-H )^2+p₀ (L₀-H )-L₀ p₀=0

Step-by-step solution

gathered p₁=p₂ p₀+ g (L₀-H )=p gathered Now, applying p₁ V₁=p₂ V₂ for the air inside the cylinder, we have p₀ (L₀ )=p (L₀-H ) p= p₀ L₀ L₀-H Substituting in Eq. (i), we have p₀+ g (L₀-H )= p₀ L₀ L₀-H or g (L₀-H )^2+p₀ (L₀-H )-p₀ L₀=0 Option (c) is correct.

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