A non - conducting piston of mass m and are `S_(0)` divides a non - conducting, closed cylinder as shown in the figure. A piston having mass m is connected with the top wall of the cylinder by a spring of force constant k. The top part is evacuated and the bottom part is evacuated and the bottom part contains an ideal gas at a pressure `P_(0)` in the equilibrium position. Adiabatic exponent `gamma` and in equilibrium length of each part is l. (neglect friction). Find the angular frequency for small oscillation.

Options

A. `(sqrt(kl+gammaP_(0)S_(0)))/(2nl)`
B. `(sqrt(3kl+gammaP_(0)S_(0)))/(ml)`
C. `sqrt((k)/(m))`
D. `(sqrt(kl +gammaP_(0)S_(0)))/(ml)`

Answer

D