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 $3.6 \times 10^{-5} \, ^oC^{-1}$).

Why does the density of solid substances change with an increase in temperature?

At a certain temperature,rod $A$ and rod $B$ of different materials have lengths $L_A$ and $L_B$ respectively. Their coefficients of linear expansion are $\alpha_A$ and $\alpha_B$ respectively. It is observed that the difference between their lengths remains constant at all temperatures. The ratio $L_A / L_B$ is given by

$A$ thin copper wire of length $l$ metre increases in length by $2\%$ when heated through $10^{\circ}C$. The percentage increase in area when a square copper sheet of side $l$ metre is heated through $10^{\circ}C$ is:

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

Two rods,one of copper $(Cu)$ and the other of iron $(Fe)$,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 of $Cu$ and $Fe$ are $\alpha_c$ and $\alpha_i$ respectively. If the length of each rod increases by the same amount when their temperatures are raised by $t^{\circ}C$,then the ratio $\frac{L_1-L_2}{L_1+L_2}$ will be: