$A$ metal cube is embedded inside a block of ice that is floating on the surface of water. The ice melts completely, and the metal cube sinks into the water. What happens to the water level in the container?

The loss in weight of a solid when immersed in a liquid at $0^o C$ is $W_0$ and at $t^o C$ is $W$. If the cubical coefficients of expansion of the solid and the liquid are $\gamma_s$ and $\gamma_l$ respectively,then $W$ is equal to:

An object of mass $10 \ kg$ is released from rest in a liquid. If the object moves a distance of $2 \ m$ while sinking in a time duration of $1 \ s$,then the mass of the liquid displaced by the submerged object is $(g = 10 \ m/s^2)$. (in $kg$)

$A$ 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

$A$ block of iron contains a hollow cavity as shown below. The block weighs $6000 \,N$ in air and $4000 \,N$ in water. If the densities of iron and water are $6 \,g/cm^3$ and $1 \,g/cm^3$ respectively, then the volume of the cavity is (assume $g = 10 \,m/s^2$): (in $\,m^3$)

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