Coefficient of cubical expansion of a metal cube is $\text{'}\gamma \text{'}$  increase in temperature  for which the volume of the cube increases by 5% is  $\raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$\gamma $}\right.$ where  $x=$

 $\mathrm{final} \mathrm{volume} {\mathrm{V}}_2=\mathrm{V}+\frac{5}{100}\mathrm{V}$

$\mathrm{V} \mathrm{is} \mathrm{initial} \mathrm{volume}$

 ${\mathrm{V}}_2=\frac{105}{100}\mathrm{V}$

${\mathrm{V}}_2=1.05\mathrm{V}; \mathrm{here} {\mathrm{V}}_1=\mathrm{V}=\mathrm{initial} \mathrm{volume}$

$\mathrm{coefficient} \mathrm{of} \mathrm{cubical} \mathrm{expansion} \mathrm{\gamma }=\frac{{\mathrm{V}}_2-{\mathrm{V}}_1}{{\mathrm{V}}_1\mathrm{\Delta T}}$

$\Rightarrow {\mathrm{V}}_2={\mathrm{V}}_1\left[1+\mathrm{\gamma \Delta T}\right]$

$1.05\mathrm{v}=\mathrm{v}\left[1+\mathrm{\gamma \Delta T}\right]$

$0.05=\gamma \Delta T$

$$\begin{gathered} \Rightarrow \Delta T=\frac{0.05}{\gamma } \\ \Rightarrow x=0.05 \end{gathered}$$