A block of wood floats in water with $\frac{4}{5}^{th}$ of its volume submerged, but it just floats in another liquid. The density of liquid is $($in $kg / m ^3 )$
Medium
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$\frac{4}{5} v_b \times \rho_w \times g=v_b \times \rho_b \times g \left\{\begin{array}{l}\text { Where, } \\ v_b=\text { volume of block } \\ \rho_w=\text { density of water }=1000\,kg / m ^3 \\ \rho_b=\text { density of block }\end{array}\right.$
$\Rightarrow \frac{\rho_w}{\rho_b}=\frac{5}{4}$
$\rho_b=\frac{4}{5} \times 1000=800 \,kg / m ^3$
And when block is put in liquid of density $\rho_f$ it just floats
$\text { So, } v_b \times \rho_b \times g=v_b \times \rho_l \times g$
$\Rightarrow \rho_b=\rho_l$
$\text { So, } \rho_l=800 \,kg / m ^3$
$\Rightarrow \frac{\rho_w}{\rho_b}=\frac{5}{4}$
$\rho_b=\frac{4}{5} \times 1000=800 \,kg / m ^3$
And when block is put in liquid of density $\rho_f$ it just floats
$\text { So, } v_b \times \rho_b \times g=v_b \times \rho_l \times g$
$\Rightarrow \rho_b=\rho_l$
$\text { So, } \rho_l=800 \,kg / m ^3$
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