$A$ cube of side $40 \ cm$ is floating with $\frac{1}{4}$th of its volume immersed in water. When a circular disc is placed on the cube,it floats with $\frac{2}{5}$th of its volume immersed in water. The mass of the disc is (in $kg$)

$A$ block of wood of volume $V$ floats in water with half of its volume submerged. The same block floats in an oil with $0.8 \,V$ volume submerged. If the density of water is $1000 \,kg \,m^{-3}$, then the density of the oil is

Two bodies are in equilibrium when suspended in water from the arms of a balance. The mass of one body is $36 \ g$ and its density is $9 \ g/cm^3$. If the mass of the other is $48 \ g$,its density in $g/cm^3$ is:

$A$ wooden block of density $0.5 \ g/cc$ is tied to a string. The other end of the string is fixed to the bottom of a tank. The tank is filled with a liquid of density $1 \ g/cc$. If the tension of the string is $20 \ N$,then the mass of the block is (Take $g = 10 \ m/s^2$) (in $kg$)

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

$A$ thin uniform cylindrical shell,closed at both ends,is partially filled with water. It is floating vertically in water in a half-submerged state. If $\rho_c$ is the relative density of the material of the shell with respect to water,then the correct statement is that the shell is