Solids expand on heating because ................

The volume of a metal sphere increases by $0.15\%$ when its temperature is raised by $24\,^{\circ}C$. The coefficient of linear expansion of the metal is:

An iron tyre is to be fitted onto a wooden wheel $1 \, m$ in diameter. The diameter of the tyre is $6 \, mm$ smaller than that of the wheel. The tyre should be heated so that its temperature increases by a minimum of ........ $^oC$ (the coefficient of cubical expansion of iron is $3.6 \times 10^{-5} \, ^oC^{-1}$).

Two different wires having lengths $L_{1}$ and $L_{2}$ and respective temperature coefficients of linear expansion $\alpha_{1}$ and $\alpha_{2}$ are joined end-to-end. Then the effective temperature coefficient of linear expansion is

Two rods,one made of aluminium and the other made of steel,having initial lengths $l_1$ and $l_2$ respectively,are connected together to form a single rod of length $(l_1 + l_2)$. The coefficients of linear expansion for aluminium and steel are $\alpha_1$ and $\alpha_2$ respectively. If the length of each rod increases by the same amount when their temperature is raised by $t^oC$,then the ratio $l_1/(l_1 + l_2)$ is:

$A$ cuboid $ABCDEFGH$ is anisotropic with $\alpha_x = 1 \times 10^{-5} /^{\circ}C$,$\alpha_y = 2 \times 10^{-5} /^{\circ}C$,$\alpha_z = 3 \times 10^{-5} /^{\circ}C$. The coefficient of superficial expansion of the faces can be: