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An ideal gas enclosed in a vericle cylin...

An ideal gas enclosed in a vericle 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 equlibrium the, volume of the gas is `V_(0)` and its pressure is `P_(0)`. The piston is slightly displaced from the equlibrium position and released. Assuming tht the system is completely isolated from its surrounding, the piston executes a simple harmonic motion and 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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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

Find the time period of mass M when displaced from its equilibrium position and then released for the system shown in figure. .

Knowledge Check

  • The volume of gas is reduced to half from its original volume. The specific heat will be

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