A closed and isolated cylinder contains ideal gas. An adiabatic separator of mass m, cross sectional area `A` divides the cylinder into two equal parts each with volume `V_(0)` and pressure `P_(0)` in equilibrium Assume the sepatator to move without friction.
The time period of oscillation for small displacements of the piston is

Options

A. `2pisqrt((mV_(0))/(2P_(0)gammaA^(2))`
B. `2pisqrt((mV_(0))/(4P_(0)gammaA^(2))`
C. `2pisqrt((mV_(0)(gamma-1))/(2P_(0)gammaA^(2))`
D. none of these

Answer

A

Explanation

Form force fine restoring force constant. And then use expression for time period