An ideal gas enclosed in a vertical cylindrical container supports a freely moving…

PHYSICS · Single correct · CBSE · Physics · Oscillations · Oscillations

Problem

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass MM . The piston and the cylinder have equal cross sectional area AA . When the piston is in equilibrium, the volume of the gas is V0V_0 and its pressure is P0P_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 (1) 12πAγP0V0M\frac{1}{2\pi} \sqrt{\frac{A\gamma P_0}{V_0 M}} (2) 12πV0MP0A2γ\frac{1}{2\pi} \sqrt{\frac{V_0 M P_0}{A^2 \gamma}} (3) 12πA2γP0MV0\frac{1}{2\pi} \sqrt{\frac{A^2 \gamma P_0}{M V_0}} (4) 12πMV0AγP0\frac{1}{2\pi} \sqrt{\frac{M V_0}{A \gamma P_0}}

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