Correct Answer is Option (C)

Let l be the length of block immersed in liquid as shown in the figure. When the block is floating,



$\therefore$ mg = Al$\rho$m

If the block is given vertical displacement y then the effective restoring force is

$F=-\left[A\left(l+y\right)\rho g-mg\right]$

$=-\left[A\left(l+y\right)\rho g-Al\rho g\right]=-Al\rho gy$

Restoring force = $-\left[Al\rho g\right]y$. As this F is directed towards its equilibrium position of block, so if the block is left free, it will execute simple harmonic motion.

Here inertia factor = mass of block = m
Spring factor = $A\rho g$

$\therefore$ Time period = $T=2\pi \sqrt{\frac{m}{A\rho g}}$   i.e. $T\propto \frac{1}{\sqrt{A}}$