Question

When a cube of wood floats in water, 60% of its volume is submerged. When the same cube floats in an unknown fluid 85% of its volume is submerged. Find the densities of wood and the unknown fluid.

Answer 1

Fraction of volume immersed is given by
$f=\frac{{\rho }_s}{{\rho }_I}$
In first case $0.6=\frac{{\rho }_s}{{\rho }_w}=\frac{{\rho }_s}{I}$
or ${\rho }_s=0.6$ g/cm${}^3$=density of wood
In second case
$0.8=\frac{{\rho }_s}{{\rho }_I}=\frac{0.6}{{\rho }_e}$
or ${\rho }_I=\frac{0.6}{0.85}$
$=0.705$ g/cm${}^3$