$A$ cork of density $0.5 \, g/cm^3$ floats on a calm swimming pool. The fraction of the cork's volume which is under water is ........ $\%$

State and prove Archimedes' principle.

$A$ 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:

$A$ body floats in a liquid contained in a beaker. The whole system,as shown,falls freely under gravity. The upthrust on the body due to the liquid is

Two rods of the same material and length have their electric resistance in the ratio $1:2$. When both rods are dipped in water,the correct statement will be:

An iceberg of density $900 \ kg/m^3$ is floating in water of density $1000 \ kg/m^3$. The percentage of the volume of the iceberg outside the water is ...... $\%$