If two rods of length $L$ and $2L$ having coefficients of linear expansion $\alpha$ and $2\alpha$ respectively are connected so that total length becomes $3L$, the average coefficient of linear expansion of the composition rod equals:

The volume of a gas at $20°C$ is $100 \,cm^3$ at normal pressure. If it is heated to $100°C$, its volume becomes $125\, cm^3$ at the same pressure, then volume coefficient of the gas at normal pressure is

A steel rod of diameter $1\,cm$ is clamped firmly at each end when its temperature is $25\,^oC$ so that it cannot contract on cooling. The tension in the rod at $0\,^oC$ is approximately ......... $N$ $(\alpha = 10^{-5}/\,^oC,\,\,Y = 2 \times 10^{11}\,N/m^2)$

A metal ball immersed in alcohol weighs ${W_1}$ at $0°C$ and ${W_2}$ at $59°C.$ The coefficient of cubical expansion of the metal is less than that of alcohol. Assuming that the density of metal is large compared to that of alcohol, it can be shown that

A rod of silver of $100\;cm$ is at $0^{\circ} C$ is heated to $100^{\circ} C$. Its length is increased by $0.19 \,cm .$ Coefficient of cubical expansion of the silver rod is

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