$A$ small metal sphere of density $\varrho$ is dropped from height $h$ into a jar containing liquid of density $\sigma$ $(\sigma > \varrho)$. The maximum depth up to which the sphere sinks is (Neglect damping forces).

$A$ 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 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

An iceberg floats in water with part of it submerged. What is the fraction of the volume of the iceberg submerged,if the density of ice is $\rho_{i} = 0.917 \ g \ cm^{-3}$ and the density of water is $\rho_{w} = 1.00 \ g \ cm^{-3}$?

$A$ cubical block is floating in a liquid with half of its volume immersed in the liquid. When the whole system accelerates upwards with a net acceleration of $g/3$,the fraction of volume immersed in the liquid will be:

$A$ 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? ....... $cm$