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Question

A cylindrical conducting piston of mass M slides smoothly inside a long cylinder closed at one end, enclosing a certain mass of a gas. The cylinder is kept with its axis horizontal. If the piston is disturbed from its equilibrium position, it oscillates simple harmonically. The period of oscillation will be (process is isothermal)

  1. 2πMhPA
  2. 2πMAPh
  3. 2πMPhA
  4. 2πMPAh


Solution

The correct option is A 2πMhPA
Extra force = (PP0)A=Ma
P1V1=P2V2
P0hA=P(hx)A 
P=P0hhx
So acceleration = (P0hhxP0)AM

a=P0AxM(hx)
For small x,
a=P0AxMh
ω2x=P0AxMh
ω=MhP0A

T=2πP0AMh


 

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