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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
\( \mathrm{P} \) 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
[JEE (Mains) 2013]
(a) \( \frac{1}{2 \pi} \frac{A \gamma P_{0}}{V_{0} M} \)
(b) \( \frac{1}{2 \pi} \frac{V_{0} M P_{0}}{A^{2} \gamma} \)
(c) \( \frac{1}{2 \pi} \sqrt{\frac{A^{2} \gamma P_{0}}{M V_{0}}} \)
(d) \( \frac{1}{2 \pi} \sqrt{\frac{M V_{0}}{A \gamma P_{0}}} \)
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