Two bodies placed on a balance are in equilibrium when immersed in water. If the mass of the first body is $36 \, g$ and its density is $9 \, g/cm^{3}$,and the mass of the second body is $48 \, g$,what is the density of the second body in $g/cm^{3}$?

$A$ hollow spherical shell of outer radius $R$ floats just submerged under the water surface. The inner radius of the shell is $r$. If the specific gravity of the shell material is $\frac{27}{8}$ with respect to water,the value of $r$ is $......R$.

The weight of a body in water is one-third of its weight in air. The density of the body is ....... $g/cm^3$. (in $.5$)

$A$ piece of metal weighs $45 \ g$ in air and $25 \ g$ in a liquid of density $1.5 \times 10^3 \ kg \ m^{-3}$ kept at $30^{\circ} C$. When the temperature of the liquid is raised to $40^{\circ} C$, the metal piece weighs $27 \ g$. The density of the liquid at $40^{\circ} C$ is $1.25 \times 10^3 \ kg \ m^{-3}$. The coefficient of linear expansion of the metal is:

In which case does the potential energy decrease?

Two cubes of size $1.0 \ m$ sides,one of relative density $0.60$ and another of relative density $1.15$ are connected by a weightless wire and placed in a large tank of water. Under equilibrium,the lighter cube will project above the water surface to a height of ........ $cm$.