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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)

A
2πMhPA
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B
2πMAPh
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C
2πMPAh
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D
2πMPhA
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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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