Physics - Gravitation Question with Solution | TestHub

Gravitational force on each due to other three particles provides the necessary centripetal force.




$\therefore \sqrt{2}\frac{G{M}^2}{{\left(\sqrt{2}\mathrm{ }R\right)}^2}\cos 45°+\frac{G{M}^2}{\left(2R\right){ }^2}=\frac{M{v}^2}{R}$

Simplifying it, we get

$V=\sqrt{\frac{\mathit{G}\mathit{M}}{\mathit{R}}\left(\frac{2\sqrt{2}+1}{4}\right)}$