$A$ metallic block of density $5 \, g \, cm^{-3}$ and having dimensions $5 \, cm \times 5 \, cm \times 5 \, cm$ is weighed in water. Its apparent weight will be

$A$ ball rises to the surface at a constant velocity in a liquid whose density is $3$ times greater than that of the material of the ball. The ratio of the force of friction acting on the rising ball to its weight is (in $: 1$)

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

The ratio of masses of a cubical block of wood and a chunk of concrete is $\frac{3}{5}$ so that the combination just floats with its entire volume submerged under water. If the specific gravity of wood is $0.5$,then the specific gravity of concrete will be:

$A$ 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:

$A$ sphere of solid material of relative density $9$ has a concentric spherical cavity and floats just submerged in water. If the radius of the sphere is $R$,then the radius of the cavity $(r)$ is related to $R$ as: