$A$ sphere of relative density $\sigma$ and diameter $D$ has a concentric cavity of diameter $d$. The ratio of $\frac{D}{d}$,if it just floats on water in a tank,is:

What is buoyant force?

Two pieces of metal when immersed in a liquid have equal upthrust on them; then

$A$ uniform solid cylinder of density $0.8 \ g/cm^3$ floats in equilibrium in a combination of two non-mixing liquids $A$ and $B$ with its axis vertical. The densities of liquids $A$ and $B$ are $0.7 \ g/cm^3$ and $1.2 \ g/cm^3$,respectively. The height of liquid $A$ is $h_A = 1.2 \ cm$ and the length of the part of the cylinder immersed in liquid $B$ is $h_B = 0.8 \ cm$. Then the length of the part of the cylinder in air is ....... $cm$.

$A$ body of density $\rho$ is dropped from rest from a height $h$ into a lake of density $\sigma$,where $\sigma > \rho$. Neglecting all dissipative forces,the maximum depth to which the body sinks before returning to float on the surface is:

$A$ cubical block of steel of each side equal to $l$ is floating on mercury in a vessel. The densities of steel and mercury are $\rho_s$ and $\rho_m$. The height of the block above the mercury level is given by: