Past exam of the mathematics course of the University of Cambridge / 2022 / ia / Paper 4 / 9C / c / i / Solution

At a point $(0,0,z)$, the two particles are at equal distance $\sqrt{a^2+z^2}$. Their force components in the rotating $xy$-plane cancel, while their $z$-components add. Hence a particle initially moving along the $z$-axis remains on it, andCancelling $m_3$ gives