A thin uniform ring of mass $6.0 \times 10^{20}\ \text{kg}$ and radius $R = 100\ \text{km}$ floats in space, far from other bodies. A small rock is released from rest on the ring's axis, at a distance $\sqrt3\,R$ from its centre O, as shown in the figure. Take $G = 6.67 \times 10^{-11}\ \text{N m}^2/\text{kg}^2$. With what speed does the rock pass through O?

Fig. 1: A thin ring of mass 6.0 times 10 to the power 20 kg and radius R equal to 100 km, seen in perspective, with centre O. A small rock P lies on the ring's axis at a distance root 3 times R from O.