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 \(\times \mathrm{g}\)
\(\therefore \quad \mathrm{abc} \times \mathrm{d} \times \mathrm{g}=\mathrm{bc} l \times 1 \times \mathrm{g}\)
\(\begin{gathered}
\quad l=\mathrm{da} \\
\therefore \quad \mathrm{~T}=2 \pi \sqrt{\frac{\mathrm{ad}}{\mathrm{~g}}}
\end{gathered}\)
\(\ldots(\text { mass }=\text { volume } \times \text { density })\)