A piece of wood has length, breadth and height, ' $a$ ', 'b' and ' $c$ ' respectively. Its relative density…
A piece of wood has length, breadth and height, ' $a$ ', 'b' and ' $c$ ' respectively. Its relative density is ' $d$ '. It is floating in water such that the side ' $a$ ' is vertical. It is pushed down a little and released. The time period of S.H.M. executed by it is ( $g=$ acceleration due to gravity)
Time period of SHM of small vertical oscillations in liquid is given by
$\mathrm{T}=2 \pi \sqrt{\frac{l}{\mathrm{~g}}}$ where $l$ is the length of piece of wood
Weight of wood $=$ weight of water displaced
$\therefore \quad$ Mass of wood $\times \mathrm{g}=$ Mass of water displaced $\times \mathrm{g}$
$\therefore \quad \mathrm{abc} \times \mathrm{d} \times \mathrm{g}=\mathrm{bc} l \times 1 \times \mathrm{g}$
$\begin{gathered}
\quad l=\mathrm{da} \\
\therefore \quad \mathrm{~T}=2 \pi \sqrt{\frac{\mathrm{ad}}{\mathrm{~g}}}
\end{gathered}$
$\ldots(\text { mass }=\text { volume } \times \text { density })$