To keep constant time,watches are fitted with a balance wheel made of:

The coefficient of volume expansion of a material is $5 \times 10^{-4} {^{\circ}C}^{-1}$. The fractional change in its density for a $40^{\circ}C$ rise in temperature is nearly.

The length of a metal rod at $30^{\circ} C$ is $30 \ cm$. If its temperature is raised to $105^{\circ} C$,its length is increased by $0.027 \ cm$. Then the coefficient of linear expansion of the metal is

$A$ simple pendulum made of a bob of mass $m$ and a metallic wire of negligible mass has a time period $2 \ s$ at $T = 0 \ ^oC$. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature,the resulting graph is a line of slope $S$. If the coefficient of linear expansion of the metal is $\alpha$,then the value of $S$ is:

The coefficient of linear expansion of a crystalline substance in one direction is $2 \times 10^{-4} /{ }^{\circ} C$ and in every direction perpendicular to it is $3 \times 10^{-4} /{ }^{\circ} C$. The coefficient of cubical expansion of the crystal is equal to ........... $\times 10^{-4} /{ }^{\circ} C$.

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