Two solids $A$ and $B$ float in water. It is observed that $A$ floats with half its volume immersed and $B$ floats with $2/3$ of its volume immersed. Compare the densities of $A$ and $B$.

$A$ wooden cube first floats inside water when a $200\,g$ mass is placed on it. When the mass is removed,the cube rises $2\,cm$ above the water level. The side of the cube is ........ $cm$.

$A$ wooden block is floating on water kept in a beaker. $40 \%$ of the block is above the water surface. Now the beaker is kept inside a lift that starts going upward with acceleration equal to $g / 2$. The block will then

$A$ beaker containing water is placed on the platform of a spring balance. The balance reads $1.5 \, kg$. $A$ stone of mass $0.5 \, kg$ and density $500 \, kg/m^3$ is immersed in water without touching the walls of the beaker. What will be the balance reading now?

$A$ sphere of diameter $7 \, cm$ and mass $266.5 \, g$ floats in a bath of a liquid. As the temperature is raised,the sphere just begins to sink at a temperature $35^{\circ} C$. If the density of the liquid at $0^{\circ} C$ is $1.527 \, g/cm^3$,then neglecting the expansion of the sphere,the coefficient of cubical expansion of the liquid is:

$A$ body weighs $50 \,g$ in air and $40 \,g$ in water. How much would it weigh in a liquid of specific gravity $1.5$ (in $\,g$)?