An object of volume $V_0$ and density $d_0$ is placed in a liquid of density $d$. What fraction of its volume remains outside the liquid?

$A$ cubical block of side $0.5\,m$ floats on water with $30\%$ of its volume under water. What is the maximum weight (in $kg$) that can be put on the block without fully submerging it under water? [Take density of water $= 10^3\,kg/m^3$]

$A$ rectangular block is $5 \ cm \times 5 \ cm \times 10 \ cm$ in size. The block is floating in water with the $5 \ cm$ side vertical. If it floats with the $10 \ cm$ side vertical,what change will occur in the level of water?

At what depth does a body remain in equilibrium in a liquid? Explain.

$A$ 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

$A$ 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