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

$A$ bimetallic strip is made of aluminium and steel $(\alpha_{Al} > \alpha_{\text{steel}})$. On heating,the strip will

$A$ solid expands upon heating because

$A$ blacksmith fixes an iron ring on the rim of the wooden wheel of a horse cart. The diameter of the rim and the iron ring are $5.243\; m$ and $5.231\; m$,respectively at $27^{\circ}C$. To what temperature (in $^{\circ}C$) should the ring be heated so as to fit the rim of the wheel? (Given: coefficient of linear expansion of iron $\alpha = 1.20 \times 10^{-5} K^{-1}$)

Find the ratio of the length of a steel rod and a copper rod if the steel rod is $4 \ cm$ longer than the copper rod at any temperature. $[$The coefficients of linear expansion for steel and copper are $1.1 \times 10^{-5} /^{\circ} C$ and $1.7 \times 10^{-5} /^{\circ} C$ respectively$]$

Obtain the relation between the coefficient of volume expansion $(\alpha_V)$ and the coefficient of linear expansion $(\alpha_l)$.