A solid cylinder of density $\rho_0$, cross-section area $A$ and length $l$ floats in a liquid $\rho(> \rho_0)$ with its axis vertical, as shown. If it is slightly displaced downward and released, the time period will be
Medium
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Let length of submerged part $=\mathrm{h}$
then $\mathrm{Ah} \rho=\mathrm{A} \ell \rho_{0}$
$\Rightarrow \mathrm{h}=\frac{\rho_{0} \ell}{\rho}$
$\therefore \mathrm{T}=2 \pi \sqrt{\frac{\mathrm{h}}{\mathrm{g}}} \Rightarrow \mathrm{T}=2 \pi \sqrt{\frac{\rho_{0} \ell}{\rho \mathrm{g}}}$
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