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
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)(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)))`
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C
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Consider an ideal gas enclosed in a vertical cylindrical container supported by a freely moving piston of mass M. When the piston is in equilibrium, the volume of the gas is V _(0) and its pressure is Po. The piston is slightly displaced from the equilibrium position and released. Frequency of SHM (simple harmonic motion) of piston is (1)/(2pi) sqrt (( gamma p _(0) A ^(N))/( M ^(q) V _(0))). What is the value of (q)/(N) = ?
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An ideal gas enclosed in a vertical cylindrical container supports a freely moving pistion of mass M. The pistion and the cylinder have equal cross sectional area A. When the pistion is in equilibrium, the volume of the gas is V_(0) and its pressure is P_(0) . The pistion is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the pistion executes a simple harmonic motion with frequency
An ideal gas enclosed in a vertical cylindrical container supports a freely moving pistion of mass M. The pistion and the cylinder have equal cross sectional area A. When the pistion is in equilibrium, the volume of the gas is V_(0) and its pressure is P_(0) . The pistion is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the pistion executes a simple harmonic motion with frequency
A
`(1)/(2pi) (A gamma P_(0))/(V_(0) M)`
B
`(1)/(2pi) (V_(0)MP_(0))/(A^(2) gamma)`
C
`(1)/(2pi) sqrt((A^(2) gamma P_(0))/(MV_(0)))`
D
`(1)/(2pi) sqrt((MV_(0))/(A gamma P_(0)))`
An ideal gas is enclosed in a vertical cylindrical container and supports a freely moving piston of mass M. The piston and the cylinder have an equal cross-sectional area A. Atmospheric pressure is p_(0) and when the piston is in equilibrium, the volume of the gas is V_(0) . The piston is now displaced slightly from its equilibrium position. Assuming that the system, is completely isolated from, its surroundings, what is the frequency of oscillation.
An ideal gas is enclosed in a vertical cylindrical container and supports a freely moving piston of mass M. The piston and the cylinder have an equal cross-sectional area A. Atmospheric pressure is p_(0) and when the piston is in equilibrium, the volume of the gas is V_(0) . The piston is now displaced slightly from its equilibrium position. Assuming that the system, is completely isolated from, its surroundings, what is the frequency of oscillation.
A
`f=(1)/(2pi)sqrt((gamma(p_(0)A^(2)+MgA))/(V_(0)M))`
B
`f=(1)/(2pi)sqrt((1)/(gamma)((p_(0)A^(2)+MgA))/(V_(0)M))`
C
`f=(1)/(2pi)sqrt(((p_(0)A^(2)+MgA))/(V_(0)M))`
D
`f=(1)/(2pi)sqrt((A(p_(0)A^(2)+MgA))/(V_(0)M))`
A closed and isolated cylinder contains ideal gas. An adiabatic separator of mass m, cross sectional area A divides the cylinder into two equal parts each with volume V_(0) and pressure P_(0) in equilibrium Assume the sepatator to move without friction. If the piston is slightly displaced by x, the net force acting on the piston is
A closed and isolated cylinder contains ideal gas. An adiabatic separator of mass m, cross sectional area A divides the cylinder into two equal parts each with volume V_(0) and pressure P_(0) in equilibrium Assume the sepatator to move without friction. If the piston is slightly displaced by x, the net force acting on the piston is
A
`(P_(0)gammaA^(2)x)/(V_(0))`
B
`(2P_(0)gammaA^(2)x)/(V_(0))`
C
`(3P_(0)gammaA^(2)x)/(V_(0))`
D
`(P_(0)gammaA^(2)x)/((gamma-1)V_(0))`
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