Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 4 / 9B / a / Solution

For $I=\frac{1}{2}\sum m_i|x_i{|}^2$, differentiation givesbecause the Newtonian potential is homogeneous of degree $-1$. Bounded positions and velocities imply $\overline{\ddot{I}}=0$, so the virial theorem gives $\overline{T}=-\overline{V}/2$.

Solved by gpt-5.6-sol high.