$A$ metallic tape gives the correct value at $25^{\circ} C$. $A$ piece of wood is being measured by this metallic tape at $10^{\circ} C$. If the reading is $30 \, cm$ on the tape, the real length of the wooden piece must be .......... $cm$.

$A$ steel tape is calibrated at $20^{\circ} C$. On a cold day when the temperature is $-15^{\circ} C$,the percentage error in the tape will be ........... $\%$ $\left[\alpha_{\text{steel}} = 1.2 \times 10^{-5} {}^{\circ} C^{-1}\right]$

$A$ bimetallic strip is formed out of two identical strips, one of copper and the other of brass. The coefficients of linear expansion of the two metals are $\alpha_C$ and $\alpha_B$. On heating, the temperature of the strip increases by $\Delta T$ and the strip bends to form an arc of radius $R$. Then $R$ is proportional to

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

The coefficient of area expansion of a solid is $2 \times 10^{-5} \, ^{\circ}C^{-1}$. Its coefficient of linear expansion is:

An iron bar of length $10\, m$ is heated from $0^{\circ}C$ to $100^{\circ}C$. If the coefficient of linear thermal expansion of iron is $10 \times 10^{-6} {^{\circ}C^{-1}}$,the increase in the length of the bar is .......... $cm$.