$A$ $400 \ g$ solid cube having an edge of length $10 \ cm$ floats in water. How much volume of the cube is outside the water (in $cm^3$)? (Given: density of water $= 1000 \ kg/m^3$)

$A$ small wooden ball of density $\rho$ is immersed in water of density $\sigma$ to a depth $h$ and then released. The height $H$ above the surface of water up to which the ball will jump out of water is

$A$ sphere of material of relative density $8$ has a concentric spherical cavity and just sinks in water. If the radius of the sphere is $2 \ cm$,then the volume of the cavity is

$A$ hemispherical portion of radius $R$ is removed from the bottom of a cylinder of radius $R$. The volume of the remaining cylinder is $V$ and mass $M$. It is suspended by a string in a liquid of density $\rho$,where it stays vertical. The upper surface of the cylinder is at a depth $h$ below the liquid surface. The force on the bottom of the cylinder by the liquid is

An ice cube contains a large air bubble. The cube is floating on the horizontal surface of water contained in a trough. What will happen to the water level when the cube melts?

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 $\rho_{i} = 0.917 \ g \ cm^{-3}$ and the density of water is $\rho_{w} = 1.00 \ g \ cm^{-3}$?