$A$ cubical block of density $\rho_{b} = 600 \ kg/m^3$ floats in a liquid of density $\rho_{l} = 900 \ kg/m^3$. If the height of the block is $H = 8.0 \ cm$, then the height of the submerged part is . . . . . . $cm$. (in $.3$)

$A$ piece of metal weighs $45 \ g$ in air and $25 \ g$ in a liquid of density $1.5 \times 10^3 \ kg \ m^{-3}$ kept at $30^{\circ} C$. When the temperature of the liquid is raised to $40^{\circ} C$, the metal piece weighs $27 \ g$. The density of the liquid at $40^{\circ} C$ is $1.25 \times 10^3 \ kg \ m^{-3}$. The coefficient of linear expansion of the metal is:

$A$ cubical block of wood of edge $10$ $cm$ and mass $0.92$ $kg$ floats in a tank of water with a layer of oil of relative density $0.6$ to a depth of $4$ $cm$ above the water. When the block attains equilibrium with four of its side edges vertical,which of the following is true?

Two solids $A$ and $B$ float in water. It is observed that $A$ floats with half its volume immersed and $B$ floats with $2/3$ of its volume immersed. Compare the densities of $A$ and $B$.

Two solids $A$ and $B$ float in water. It is observed that $A$ floats with $\frac{1}{2}$ of its body immersed in water and $B$ floats with $\frac{1}{4}$ of its volume above the water level. The ratio of the density of $A$ to that of $B$ is

$A$ cylindrical block of wood of base area $30 \, cm^2$ floats in a liquid of density $900 \, kg/m^3$. The block is depressed lightly and then released. The time period of the resulting oscillations of the block is equal to that of a spring with a block of the same mass. The spring constant is equal to ........ $N/m$.