A rectangular block of mass $m$ and area of cross-section A floats in a liquid of density $\rho$. If it is…
A rectangular block of mass $m$ and area of cross-section A floats in a liquid of density $\rho$. If it is given a small vertical displacement from equilibrium it undergoes with a time period $T$, Then:
$T \propto \frac{1}{\sqrt{m}}$
$T \propto \sqrt{\mathrm{A}}$
$T \propto \frac{1}{\sqrt{A}}$
$T \propto \frac{1}{\rho}$
Solution
Restoring force $=A \times \int g=k x$
$\begin{array}{ll}
\Rightarrow & K=A \rho g \\
\Rightarrow & T=2 \pi \sqrt{\frac{m}{A \rho g}}
\end{array}$
This shows that $T \propto \frac{1}{\sqrt{A}}$.
.