A beaker of height $H$ is made up of a material whose coefficient of linear thermal expansion is $3\alpha $ . It is filled up to the brim by a liquid whose coefficient of thermal expansion is $\alpha $. If now the beaker along with its contents is uniformly heated through a small temperature $T$ the level of liquid will reduce by (given $\alpha  << 1$) 

A solid metallic cube having total surface area $24\;m ^{2}$ is uniformly heated. If its temperature is increased by $10\,^{\circ} C$, calculate the increase in volume of the cube $\left(\right.$ Given $\left.: \alpha=5.0 \times 10^{-4}{ }^{\circ} C ^{-1}\right)$

The weight of sphere in air is $50\ g$. Its weight $40\  g$ in a liquid, at temperature $20\,^o C$. When  temperature increases to $70\,^o C$ , it weight becomes $45\  g$, then the ratio of densities of liquid at given two temperature is

A uniform cylindrical rod of length $L$ and radius $r$, is made from a material whose Young's modulus of Elasticity equals $Y$. When this rod is heated by temperature $T$ and simultaneously subjected to a net longitudinal compressional force $F$, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equals to

The coefficient of linear expansion of crystal in one direction is ${\alpha _1}$ and that in every direction perpendicular to it is ${\alpha _2}$. The coefficient of cubical expansion is

Two marks on a glass rod $10\, cm$ apart are found to increase their distance by $0.08\, mm$ when the rod is heated from $0\,^oC$ to $100\,^oC$. A flask made of the same glass as that of rod measures a volume $1000\, cc$ at $0\,^oC$. The volume it measures at $100\,^oC$ in $cc$ is