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$]$

When the temperature of a metal sphere is increased by $40^{\circ}C$,its volume increases by $0.24\%$. The coefficient of linear expansion of the metal is ....... $^{\circ}C^{-1}$.

$A$ 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 $\alpha = 1.20 \times 10^{-5} K^{-1}$)

$A$ seconds pendulum clock has a steel wire. The clock shows correct time at $25^{\circ} C$. How many seconds does the clock lose or gain in one week,when the temperature is increased to $35^{\circ} C$? (Given: $\alpha_{\text{steel}} = 1.2 \times 10^{-5} /^{\circ} C$)

$A$ hole is drilled in a copper sheet. The diameter of the hole is $4.24 \,cm$ at $27.0^{\circ} C$. What is the diameter of the hole when it is heated to $35^{\circ} C$?

Coefficient of linear expansion of brass and steel rods are $\alpha_1$ and $\alpha_2$. Lengths of brass and steel rods are $l_1$ and $l_2$ respectively. If $(l_2 - l_1)$ is maintained same at all temperatures,which one of the following relations holds good?