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A block of wood floats in water with $(4 / 5)$ th of its volume submerged. If the same block just floats in a liquid, the density of the liquid is $\left(\right.$ in $\mathrm{kgm}^{-3}$ )
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The correct answer is:
800
Applying Archimedes' principle, submerged part $=$ replaced water
$\Rightarrow \quad \frac{4}{5} h \rho_{u s} g=h \times \rho_l \times g$
where, $\rho_w=$ density of water and $\rho_l=$ density of the liquid.
$\begin{array}{ll}
\therefore & \rho_l=\frac{4}{5} \times \rho_w=\frac{4}{5} \times 1000 \\
\Rightarrow & \rho_l=800 \mathrm{kgm}^{-3}
\end{array}$
$\Rightarrow \quad \frac{4}{5} h \rho_{u s} g=h \times \rho_l \times g$
where, $\rho_w=$ density of water and $\rho_l=$ density of the liquid.
$\begin{array}{ll}
\therefore & \rho_l=\frac{4}{5} \times \rho_w=\frac{4}{5} \times 1000 \\
\Rightarrow & \rho_l=800 \mathrm{kgm}^{-3}
\end{array}$
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