$U_{T}=U_{1}+U_{2}$

$=\frac{1}{2 \mathrm{Y}}\left[\left(\frac{\mathrm{W}}{\mathrm{A}_{1}}\right)^{2} \times \mathrm{A}_{1} \times \mathrm{L}+\left(\frac{\mathrm{W}}{\mathrm{A}_{2}}\right)^{2} \times \mathrm{A}_{2} \times \mathrm{L}\right]$

$=\frac{W^{2} L}{2 Y}\left[\frac{1}{A_{1}^{2}}+\frac{1}{A_{2}^{2}}\right]$

$=\frac{W^{2} L}{2 Y}\left[\frac{1}{\pi R^{2}}+\frac{1}{\pi(2 R)^{2}}\right]$

$=\frac{W^{2} L}{2 \pi Y R^{2}}\left(1+\frac{1}{4}\right)=\frac{5 W^{2} L}{8 \pi Y R^{2}}$