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 position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency :

Question

$\begin{array}{1 1} (1)\;\large\frac{1}{2 \pi} \frac{A_{\gamma}P_0}{V_0M} \\ (2)\;\large\frac{1}{2\pi} \frac{V_0 M P_0}{A^2 \gamma} \\ (3)\;\large\frac{1}{2\pi} \sqrt{\frac{A^2 \gamma P_0}{MV_0}}\\ (4)\;\large\frac{1}{2 \pi} \sqrt{\large\frac{MV_0}{A \gamma P_0}} \end {array}$