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

On what does the value of the coefficient of linear expansion depend?

$A$ steel meter scale is to be ruled so that millimeter intervals are accurate within about $5 \times 10^{-5} \,m$ at a certain temperature. The maximum temperature variation allowable during the ruling is (Coefficient of linear expansion of steel $= 10 \times 10^{-6} \,K^{-1}$) (in $^{\circ} C$)

$A$ metal rod $2 \,m$ long increases in length by $1.6 \,mm$, when heated from $0^{\circ} C$ to $60^{\circ} C$. The coefficient of linear expansion of the metal rod is:

$A$ large steel wheel is to be fitted onto a shaft of the same material. At $27^{\circ}C$,the outer diameter of the shaft is $8.70\;cm$ and the diameter of the central hole in the wheel is $8.69\;cm$. The shaft is cooled using 'dry ice'. At what temperature (in $^{\circ}C$) of the shaft does the wheel slip on the shaft? Assume the coefficient of linear expansion of the steel to be constant over the required temperature range: $\alpha_{steel} = 1.20 \times 10^{-5}\;K^{-1}$.

The temperature of a wire of length $1 \, m$ and area of cross-section $1 \, cm^2$ is increased from $0^\circ C$ to $100^\circ C$. If the rod is not allowed to increase in length,the force required will be $(\alpha = 10^{-5} /^\circ C$ and $Y = 10^{11} \, N/m^2)$.