$A$ 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 $^{\circ} C$)

The coefficient of apparent expansion of mercury in a glass vessel is $153 \times 10^{-6} /{ }^{\circ} C$ and in a steel vessel is $144 \times 10^{-6} /{ }^{\circ} C$. If $\alpha$ for steel is $12 \times 10^{-6} /{ }^{\circ} C$, then the coefficient of linear expansion $\alpha$ for glass is:

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?

$A$ rod is found to be $0.05 \ cm$ longer at $40^{\circ} C$ than it is at $10^{\circ} C$. The length of the rod at $0^{\circ} C$ is (coefficient of linear expansion of the material of the rod $= 1.5 \times 10^{-5} \ {}^{\circ} C^{-1}$) (in $cm$)

$A$ $1$ litre glass flask contains some mercury. It is found that at different temperatures,the volume of air inside the flask remains the same. What is the volume of mercury in this flask in $cc$ if the coefficient of linear expansion of glass is $9 \times 10^{-6} /^{\circ}C$ and the coefficient of volume expansion of mercury is $1.8 \times 10^{-4} /^{\circ}C$?

Two wires $A$ and $B$ of the same length,same area of cross-section,and having the same Young's modulus are heated to the same temperature range. If the coefficient of linear expansion of wire $A$ is $3/2$ times that of wire $B$,what is the ratio of the thermal forces produced in the two wires?