An iceberg floats in water with part of it submerged. What is the fraction of the volume of the iceberg submerged if the density of ice is ${\rho _i} = 0.917 \, g/cm^3$?

$A$ solid cylinder of length $\ell$ and cross-sectional area $A$ is immersed such that it floats with its axis vertical at the liquid-liquid interface with length $\ell / 4$ in the denser liquid as shown in the figure. The lower density liquid has density $\varrho$ and the denser liquid has density $3\varrho$. The density $d$ of the solid cylinder is:

$A$ cubical block of wood with a side length of $10 \ cm$ floats at the interface between oil and water,with its lower surface horizontal and $4 \ cm$ below the interface. The density of oil is $0.6 \ g/cm^3$. The mass of the block is ......... $gm$.

$A$ hemispherical bowl just floats without sinking in a liquid of density $1.2 \times 10^3 \ kg/m^3$. If the outer diameter and the density of the bowl are $1 \ m$ and $2 \times 10^4 \ kg/m^3$ respectively,then the inner diameter of the bowl will be........ $m$.

Write the equation for the volume of the partially submerged part of a body floating on the surface of a liquid.

$A$ vessel contains oil (density = $0.8 \text{ g/cm}^3$) over mercury (density = $13.6 \text{ g/cm}^3$). $A$ homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere in $\text{g/cm}^3$ is