$A$ ball whose density is $0.4 \times 10^3 \ kg/m^3$ falls into water from a height of $9 \ cm$. To what depth does the ball sink in $cm$?

State Archimedes' principle.

$A$ wooden cube of side $10 \ cm$ floats at the interface between water and oil with its lower surface $3 \ cm$ below the interface. If the density of oil is $0.9 \ g \ cm^{-3}$,the mass of the wooden cube is (in $g$)

$A$ log of wood of mass $120 \ kg$ floats in water. The mass that can be put on the raft to make it just sink should be ....... $kg$ (density of wood = $600 \ kg/m^3$,density of water = $1000 \ kg/m^3$).

$A$ 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?

$A$ cork of density $0.5 \, g/cm^3$ floats on a calm swimming pool. The fraction of the cork's volume which is under water is ........ $\%$