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An ideal gas enclosed in a vertical cyli...

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M. the piston and the cylinder have equal cross sectional area A. when the piston is in equilibrium, the volume of the gas is `V_(0)` and its pressure is `P_(0)`. the piston is slightly displaced from the equilibrium posittion and released. assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency

A

`(1)/(2pi)(AgammaP_(0))/(V_(0)M)`

B

`(1)/(2pi)(V_(0)MP_(0))/(A^(2)gamma)`

C

`(1)/(2pi)sqrt((A^(2)gammaP_(0))/(MV_(0)))`

D

`(1)/(2pi)sqrt((MV_(0))/(AgammaP_(0)))`

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

  • An ideal gas enclosed in a cylindrical container supports a freely moving piston of mass M . The piston and the cylinder have equal cross-sectional area A . When the piston is in equilibrium, the volume of the gas is V_(0) and its pressure is P_(0) . The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency

    A
    `(1)/(2pi)sqrt((MV_(0))/(AgammaP_(0)))`
    B
    `(1)/(2pi)(AgammaP_(0))/(V_(0)M)`
    C
    `(1)/(2pi)(V_(0)MP_(0))/(A^(2)gamma)`
    D
    `(1)/(2pi)sqrt((A^(2)gammaP_(0))/(MV_(0)))`

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