Solution

ID: 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/solution

The virial theorem for a stationary isolated system with inverse-square gravity is
where is total kinetic energy in the system's centre-of-mass frame and 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.

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