If two rods of lengths $L$ and $2L$,having coefficients of linear expansion $\alpha$ and $2\alpha$ respectively are connected end-to-end,then find the average coefficient of linear expansion of the composite rod.

When a bimetallic strip is heated, it . . . . . . .

$A$ thin copper wire of length $L$ increases in length by $1\%$ when heated from temperature $T_1$ to $T_2$. What is the percentage change in area when a thin copper plate having dimensions $2L \times L$ is heated from $T_1$ to $T_2$?

$A$ rail track made of steel having length $10\,m$ is clamped on a railway line at its two ends as shown in the figure. On a summer day,due to a rise in temperature by $20\,^oC$,it is deformed as shown in the figure. Find $x$ (displacement of the centre) if $\alpha_{steel} = 1.2 \times 10^{-5} \,^oC^{-1}$.

The density of a substance at $0 \, ^\circ C$ is $10 \, g/cm^3$ and at $100 \, ^\circ C$ is $9.7 \, g/cm^3$. The coefficient of linear expansion of the substance is ..... $^\circ C^{-1}$.

$A$ uniform metal rod is used as a bar pendulum. If the room temperature rises by $10^{\circ}C$,and the coefficient of linear expansion of the metal of the rod is $2 \times 10^{-6} /^{\circ}C$,the period of the pendulum will have a percentage increase of: