Explanation

(a) Let the piston be displaced through distance $x$ towards left, then volume decreases, pressure increases. If $\mathrm{\Delta}P$ is increase in pressure and $\mathrm{\Delta}V$ is decreases in volume, then considering the process to take place gradually (i.e. isothermal)
$P_{1}V_{1} = P_{2}V_{2}$
$\Rightarrow PV = (P + \mathrm{\Delta}P)(V - \mathrm{\Delta}V)$
$\Rightarrow PV = PV + \mathrm{\Delta}PV - P\mathrm{\Delta}V - \mathrm{\Delta}P\mathrm{\Delta}V$
$\Rightarrow \mathrm{\Delta}P.V - P.\mathrm{\Delta}V = 0\ $(neglecting $\mathrm{\Delta}P.\mathrm{\Delta}V)$
$\mathrm{\Delta}P(Ah) = P(Ax) \Rightarrow \mathrm{\Delta}P = \frac{P.x}{h}$
This excess pressure is responsible for providing the restoring force $(F)$ to the piston of mass $M$
Hence $F = \mathrm{\Delta}P.A = \frac{PAx}{h}$
Comparing it with $|F| = kx \Rightarrow k = M\omega^{2} = \frac{PA}{h}$
$\Rightarrow \omega = \sqrt{\frac{PA}{Mh}} \Rightarrow T = 2\pi\sqrt{\frac{Mh}{PA}}$
Short trick: by checking the options dimensionally. Option (a) is correct