$A$ block of volume $V$ and density $\sigma_b$ is placed in a liquid of density $\sigma_l$ (where $\sigma_l > \sigma_b$). If the block is moved upward by a height $h$ while remaining completely submerged in the liquid,what is the increase in the gravitational potential energy of the system?

When does a body sink in a liquid? Explain.

$A$ 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 $g$).

$A$ body floats with $\frac{1}{n}$ of its volume outside of water. If the body is pushed to a depth $h$ inside the water and released,it will come to the surface after time $t$. Then:

$A$ wooden cylinder floats vertically in water with half of its length immersed. The density of wood 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