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 \(=2 \pi \sqrt{\frac{\text { Inertia factor }}{\text { spring factor }}}\)

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

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