A cuboidal piece of wood has dimensions $a, b$ and $c$. Its relative density is $d$. It is floating in a large body of water such that side a is vertical. It is pushed down a bit and released. The time period of $SHM$ executed by it is :
Diffcult
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Time period of $SHM$ of small vertical oscillations in a liquid is given by $T=2 \pi \sqrt{\frac{l}{g}, \text { where }}$
$l$ is the length of $cube/cylinder$ dipped in the water.
So according to law of floatation,
weight of the cube $=$ weight of the water displaced
$a b c \times d \times g=b c l \times 1 \times g$
$\Rightarrow l=d a$
$\Rightarrow T=2 \pi \sqrt{\frac{d a}{g}}$
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