$A$ 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

$A$ right circular cylinder has a mass $m$,radius $r$,and a height $h$. The cylinder is completely submerged in a fluid of density $\rho$,as shown in the diagram,and is released. What is the magnitude of the net force on the cylinder initially?

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?

$A$ block of material with density $3 \,g/cc$ is placed on a fluid of density $7 \,g/cc$. The fraction of volume of the piece of material outside the fluid is

$A$ solid sphere of radius $r$ is floating at the interface of two immiscible liquids of densities $\rho_1$ and $\rho_2$ $(\rho_2 > \rho_1)$,with half of its volume lying in each. The height of the upper liquid column from the interface of the two liquids is $h$. The force exerted on the sphere by the upper liquid is (atmospheric pressure $= p_0$ and acceleration due to gravity is $g$).

$A$ block of steel of size $5 \times 5 \times 5 \, cm^3$ is weighed in water. If the relative density of steel is $7$,its apparent weight is ........... $g wt$.