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 $\left.: \alpha=5.0 \times 10^{-4}{ }^{\circ} C ^{-1}\right)$

A steel rail of length $5\,m$ and area of cross-section $40\,cm^2$ is prevented from expanding along its length while the temperature rises by $10\,^oC$. If coefficient of linear expansion and Young's modulus of steel are $1.2\times10^{-5}\, K^{-1}$ and $2\times10^{11}\, Nm^{-2}$ respectively, the force developed in the rail is approximately

At $NTP$ water boils at $100°C.$ Deep down the mine, water will boil at a temperature

The density of water at $20^oC$ is $0.998\  gm/cm^3$ and at $40^oC$ is $0.992\ gm/cm^3$. The mean coefficient of cubical expansion (in per ${}^oC$) is

A brass wire $1.8\; m$ long at $27\,^{\circ} C$ is held taut with little tension between two rigid supports. If the wire is cooled to a temperature of $-39\,^{\circ} C ,$ what is the tension developed in the wire, if its diameter is $2.0 \;mm$ ? Co-efficient of Itnear expansion of brass $=2.0 \times 10^{-5}\; K ^{-1} ;$ Young's modulus of brass $=0.91 \times 10^{11} \;Pa$

The volume of the bulb of a mercury thermometer at $0^o C$ is $V_0$and cross section of the capillary is $A_0$. The coefficient of linear expansion of glass is $a_g$ $per ^o C$ and the cubical expansion of mercury $\gamma_m$ $per ^o C$. If the mercury just fills the bulb at $0^o C$, what is the length of mercury column in capillary at $T^o C.$