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

$A$ pendulum clock shows the correct time at $20^{\circ}C$. During summer days,when the temperature rises to $40^{\circ}C$,what will be the time change in the clock in one day (in $.64$)? (Given: $\alpha = 10^{-5} {^{\circ}C}^{-1}$)

$A$ blacksmith fixes a circular iron frame on the wooden wheel of a bullock cart. The diameters of the wooden wheel and the circular iron frame are $5.012 \ m$ and $5 \ m$ respectively at $27^{\circ} C$. The temperature (in $^{\circ} C$) to which the iron ring must be heated so as to fit the wooden wheel is (Coefficient of linear expansion of iron $= 1.2 \times 10^{-5} \ ^{\circ} C^{-1}$).

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

On heating a uniform metallic cylinder, its length increases by $3 \%$. The area of cross-section of its base will increase by ........... $\%$

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