When an air bubble rises in water,does its potential energy increase or decrease?

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

$A$ spherical ball of radius $r$ and relative density $0.5$ is floating in equilibrium in water with half of it immersed in water. The work done in pushing the ball down so that the whole of it is just immersed in water is: (where $\rho$ is the density of water)

$A$ 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

An ice block floats in a liquid whose density is less than water. $A$ part of the block is outside the liquid. When the whole of the ice has melted,the liquid level will

$A$ cylinder of mass $m$ and material density $\rho$ hanging from a string is lowered into a vessel of cross-sectional area $A$ containing a liquid of density $\sigma$ $(< \rho)$ until it is fully immersed. The increase in pressure at the bottom of the vessel is