Question

A block of wood floats in water with ${\frac{4}{5}}^{\text{th}}$ of its volume submerged but in another liquid, it floats fully submerged. The density of the unknown liquid is (in ${\text{kg/m}}^3$)

• A. $750$
• B. $800$
• C. $1000$
• D. $1250$

Answer 1

The correct option is B $800$

In first case:
Volume of fluid displaced when block is floating in water,
$V=\frac{4}{5}{V}_b$
where $V_b$ is the volume of block.
Applying the condition for floatation,
$F_b=mg$
$\Rightarrow V{\rho }_{w}g=V_b{\rho }_{b}g$
$\Rightarrow \frac{4}{5}{V}_b\times {\rho }_w\times g=V_b\times {\rho }_b\times g$
Or, $\frac{{\rho }_w}{{\rho }_b}=\frac{5}{4}$
Substituting the values,
${\rho }_b=\frac{4}{5}\times {\rho }_w$
${\rho }_b=\frac{4}{5}\times 1000=800{\text{kg/m}}^3...\left(i\right)$
When block is put in an unknown liquid of density $\rho$, it floats in a fully submerged condition.
$\Rightarrow \text{Volume of fluid displaced}=\text{volume of body}$
$\therefore V_f=V_b...\left(ii\right)$,
Applying condition of floatation:
$V_f\rho g=mg$
Or, $V_f\rho g=V_b{\rho }_{b}g...\left(iii\right)$
From Eq.$\left(i\right),\left(ii\right),\left(iii\right)$,
$\rho ={\rho }_b=800{\text{kg/m}}^3$