QJEEM24Ph3754: JEE Main 2024 Physics - Class 11 JEEM24Ph3754 Solution: Four identical particles of mass are kept at the four corners…

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