Sol. $$ \begin{aligned} & \mathrm{F}_{\text {net }}=\sqrt{2} \mathrm{~F}+\mathrm{F}^{\prime} \\ & \mathrm{F}=\frac{\mathrm{Gm}^2}{\mathrm{a}^2} \text { and } \mathrm{F}^{\prime}=\frac{G \mathrm{~m}^2}{(\sqrt{2} \mathrm{a})^2} \\ & \mathrm{~F}_{\text {net }}=\sqrt{2} \frac{\mathrm{Gm}^2}{\mathrm{a}^2}+\frac{\mathrm{Gm}^2}{2 \mathrm{a}^2} \\ & \left(\frac{2 \sqrt{2}+1}{32}\right) \frac{\mathrm{Gm}^2}{\mathrm{~L}^2}=\frac{\mathrm{Gm}^2}{\mathrm{a}^2}\left(\frac{2 \sqrt{2}+1}{2}\right) \\ & \mathrm{a}=4 \mathrm{~L} \end{aligned} $$