The ratio among the linear expansion coefficient $(\alpha)$,areal expansion coefficient $(\beta)$,and volume expansion coefficient $(\gamma)$ is:

$A$ sheet of steel at $20^{\circ} C$ has dimensions as shown in the figure. If the coefficient of linear expansion for steel is $10^{-5} {^{\circ} C}^{-1}$, what is the change in the area at $60^{\circ} C$ (in $\text{ cm}^2$)?

$A$ hole of diameter $5 \ cm$ is drilled in a metal sheet at $30^{\circ} C$. The coefficient of linear expansion of the metal is $2 \times 10^{-5} K^{-1}$. The diameter of the hole when the temperature is raised to $230^{\circ} C$ is equal to: (in $cm$)

$A$ pendulum clock shows the correct time at $20\,^oC$. The coefficient of linear expansion of the pendulum material is $12 \times 10^{-6}\,^oC^{-1}$. How much time in $sec/day$ will it lose at $40\,^oC$?

If the length of a cylinder on heating increases by $2\%$,the area of its base will increase by ....... $\%$

If the volume of a block of metal changes by $0.12\%$ when it is heated through $20^{\circ}C$,the coefficient of linear expansion (in per $^{\circ}C^{-1}$) of the metal is :-