Question

A block of wood floats in water $\left(4/5\right)th$ of its volume submerged. If the same block just floats in a liquid, the density of liquid in ${\text{kg/m}}^3$ is
(Take density of water as $1000{\text{kg/m}}^3$)

• A. $900{\text{kg/m}}^3$
• B. $400{\text{kg/m}}^3$
• C. $1250{\text{kg/m}}^3$
• D. $800{\text{kg/m}}^3$

Answer 1

The correct option is D $800{\text{kg/m}}^3$

Let $V$ be the volume of the block.
Let density of block and liquid is ${\rho }_b$ and ${\rho }_l$
When block floats in water, weight of the block will be equal to the weight of displaced water
${\rho }_{b}Vg=\left(4/5V\right)\rho g$
${\rho }_b=4/5\rho$......(1)
When block is just float in the liquid, weight of the block will be equal to the weight of displaced liquid
${\rho }_{b}Vg={\rho }_{l}Vg$
${\rho }_b={\rho }_l$.......(2)
From equation (1) and (2),
${\rho }_l=4/5\rho$
$\because \text{Density of water}\left(\rho \right)=1000{\text{kg/m}}^3$
$\therefore {\rho }_l=800{\text{kg/m}}^3$