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  4. A rectangular block of mass m and area of cross section . A floats in a liquid of density ρ. If it is given a small vertical displacement from equilibrium it undergoes oscillation with a time period T, then :

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Q. 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 oscillation with a time period $T$, then :

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Solution:

Time period of SHM of small vertical oscillations in a liquid is given
by $T =2 \pi \sqrt{\frac{1}{g}}$, where $l$ is the length of
cube/cylinder/block dipped in the liquid.
So according to law of floatation,
weight of the block $=$ weight of the liquid displaced
$mg = Al g g$
$\Rightarrow I =\frac{ m }{ Ap }$
$\Rightarrow T =2 \pi \sqrt{\frac{ m }{ Apg }}$
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