JEE Advanced2007PhysicsThermodynamicsActual
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: While the piston is at a distance 2 L from the top, the hole at the top is sealed. The pisto
Options
- A( 2 p₀ R^2 R^2 p₀+M g )(2 L)
- B( p₀ R^2-M g R^2 p₀ )(2 L)
- C( p₀ R^2+M g R^2 p₀ )(2 L)
- D( p₀ R^2 R^2 p₀-M g )(2 L)
Correct answer
D. ( p₀ R^2 R^2 p₀-M g )(2 L)
Step-by-step solution
Let p be the pressure in equilibrium Then, aligned & p=p₀- M g A =p₀- M g R^2 & Applying p₁ V₁=p₂ V₂ & p₀(2 A L)=(p) (A L^ ) & L^ = 2 p₀ L p = ( p₀ p₀- M g R^2 ) (2L) & = ( p₀ R^2 R^2 p₀-M g )(2 L) & aligned Option (d) is correct.