The height of liquid column in the cylindrical container is $h_0$, at $0{}^{\circ }\mathrm{C}$. If the temperature of liquid rises to $\theta °\mathrm{C}$, assuming the expression of both solid (container) and liquid, find the height of the liquid column. Assume ${\gamma }_l$ and ${\gamma }_s$ as the coefficient cubical expression of liquid and solid.

A solid floats in a liquid at $20°\mathrm{C}$ with $75\%$ of it immersed. When the liquid is heated to $100°\mathrm{C}$, the same solid floats with $80\%$ of it immersed in the liquid. Calculate the coefficient of expansion of the liquid. Assume the volume of the solid to be constant.

A body is floating inside a liquid. If we increases temperature then what changes occur in buoyancy force (Assume body is always in floating condition)

A metal sphere floats on mercury. The fraction of volume of the sphere submerged in mercury is $f$. The coefficients of expansion of the metal and mercury are${\gamma }_1$ and ${\gamma }_2$, the temperature of system is increased by $\mathrm{\Delta }T$. Then find the fraction of the volume of the sphere submerged in mercury at this situation.

A metal sphere floats on mercury. The fraction of volume of the sphere submerged in mercury is $f$. The coefficients of expansion of the metal and mercury are${\gamma }_1$ and ${\gamma }_2$, the temperature of system is increased by $\mathrm{\Delta }T$. Then under what conditions will the sphere sink or lift up considering expansion of solid?

A metal sphere floats on mercury. The fraction of volume of the sphere submerged in mercury is $f$. The coefficients of expansion of the metal and mercury are${\gamma }_1$ and ${\gamma }_2$, the temperature of system is increased by $\mathrm{\Delta }T$. Then if we neglect the expansion of solid, determine the temperature rise at which the solid is completely immersed?

A sinker of weight $W_0$ has an apparent weight $W_1$ when placed in a liquid at a temperature $T_1$ and $W_2$ when weighed in the same liquid at a temperature $T_2$. The coefficient of cubical expansion of the material of the sinker is ${\gamma }_s$. What is the coefficient of volume expansion of the liquid?

A cubical of coefficient of linear expansion ${\alpha }_s$, floats in the liquid of coefficient of volume expansion ${\gamma }_l$. If the depth of immersion of the cube at $0{}^{\circ }\mathrm{C}$ is $h_0$, find the depth of immersion of the cube at $\theta °\mathrm{C}$.

What is wrong with the following statement? "Given any two bodies, the one with the higher temperature contains more heat".