Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2015 / S2 / 3 / 1

The virial theorem for a stationary isolated system with inverse-square gravity iswhere $K$ is total kinetic energy in the system's centre-of-mass frame and $W$ is its negative gravitational potential energy. The brackets denote a suitable time or ensemble average. Surface pressure, rapid evolution or mass fluxes add terms, so equilibrium and an appropriate boundary are substantive assumptions.