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A non-conducting piston of mass m and are S 0 divides a non-conducting, closed cylinder as shown in the figure. A piston having mass m is connected with the top wall of the cylinder by a spring of force constant k . The top part is evacuated and the bottom part contains an ideal gas at a pressure P 0 in the equilibrium position. Adiabatic exponent γ and in equilibrium length of each part is l . (neglect friction). Fi

Options

  1. Ak l + γ P 0 S 0 2 n l
  2. B3 k l + γ P 0 S 0 m l
  3. Ck m
  4. Dk l + γ P 0 S 0 m l

Correct answer

D. k l + γ P 0 S 0 m l

Step-by-step solution

P V γ = c d p P + γ d V V = 0 ⇒ d P =   - γ P 0 V d V Restoring force F = k d x + S 0 d P ⇒ a = - k l + γ S 0 P 0 m l d x ω = k l + γ P 0 S 0 m l

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