An ideal monoatomic gas is enclosed in a fixed horizontal adiabatic cylinder of cross sectional area A. The cylinder is fitted with an adiabatic piston of mass m (attached to one end of a spring as shown) which can move horizontally without friction inside the cylinder. In equilibrium, the spring is in natural length and pressure and volume are `P_0` and `V_0` respectively. The piston is slightly displaced from equilibrium and released. Then, frequency of small oscillation is

Options

A. `1/(2pi)sqrt(k/m+5/3 (P_0A^2)/(mV_0))`
B. `1/(2pi)sqrt(k/m-5/3 (P_0A^2)/(mV_0))`
C. `1/(2pi)sqrt(5/3 (P_0A^2)/(mV_0)-k/m)`
D. `1/(2pi)sqrt(k/m)`

Answer

A