$A$ 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 $kg$)

An ice block contains a glass ball. When the ice melts within a vessel containing water,the level of the water

$A$ body of volume $V$ floats on water with $\frac{1}{3}$ of its volume above the surface. The volume of the object above the surface when floating on a liquid of specific gravity $1.5$ is

$A$ cylindrical block floats vertically in a liquid of density $\rho_{1}$ kept in a container such that the fraction of volume of the cylinder inside the liquid is $x_{1}$. Then some amount of another immiscible liquid of density $\rho_{2} (\rho_{2} < \rho_{1})$ is added to the liquid in the container so that the cylinder now floats just fully immersed in the liquids with $x_{2}$ being the fraction of volume of the cylinder inside the liquid of density $\rho_{1}$. The ratio $\rho_{1} / \rho_{2}$ will be

$A$ hollow cone floats with its axis vertical up to one-third of its height in a liquid of relative density $0.8$ and with its vertex submerged. When another liquid of relative density $\rho$ is filled in it up to one-third of its height,the cone floats up to half its vertical height. The height of the cone is $0.10 \ m$ and the radius of the circular base is $0.05 \ m$. The specific gravity $\rho$ is given by

Determine the equation for the volume of the partially immersed part of a body floating in a fluid.