Where, $l=$ length of part immersed in liquid.

When it is given in downward displacement $y$, restoring force (upward direction) on block is

$F=-[A(l+y) \rho g-m g]$

$=-[A(l+y) \rho g-A l \rho g]$

$=-A \rho g y$

i.e. $F \propto-y$ or $a \propto-\gamma,$ so it execute SHM (inertia factor). Mass of block $=m$

Spring factor $=A \rho g$

Time period $=2 \pi \sqrt{\frac{\text { Inertia factor }}{\text { spring factor }}}$

$T=2 \pi \sqrt{\frac{m}{A \rho g}}$

$\Rightarrow T^{2} \propto \frac{m}{A \rho}$