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A block of wood floats in water with ${\frac{4}{5}}^{t h}$ of its volume submerged. If the same block just floats in a liquid, the density of the liquid (in $k g m^{- 3}$ ) is

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Detailed Solution

$I \to$ $v ρ g_{b l o c k} = v_{0} ρ_{w a t e r} g$

$\frac{v_{o}}{v} = \frac{ρ_{b l o c k}}{ρ_{w a t e r}} = \frac{4}{5}$

$ρ_{b l o c k} = \frac{4}{5} \times ρ_{w a t e r}$

$I I \to$ $v ρ_{b l o c k} g = v ρ_{l i q u i d} g$

$ρ_{b l o c k} = ρ_{l i q u i d}$

$\Rightarrow ρ_{l i q u i d} = \frac{4}{5} \times ρ_{w a t e r} = \frac{4}{5} \times 1000 k g m^{- 3}$

$ρ_{l i q u i d} = 800 k g m^{- 3}$

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