Question

When a cube is floating in water, $20$% of the cube is outside the water. When the same cube is placed in another liquid, $35$% of the cube is outside the liquid. The density of the liquid is _________ times density of water in $g{cm}^{-3}$.

• A. $\frac{16}{13}$
• B. $\frac{4}{13}$
• C. $\frac{13}{20}$
• D. $\frac{4}{5}$

Answer 1

The correct option is A $\frac{16}{13}$

For the cube in water

${\rho }_{s}Vg={\rho }_w\left(0.8V\right)g$

For the cube in liquid

${\rho }_{s}Vg={\rho }_l\left(0.65V\right)g$

$\Rightarrow {\rho }_l=\frac{0.8}{0.65}{\rho }_w=\frac{16}{13}{\rho }_w$