The fastest possible rate of rotation of a planet is that for which the gravitational…

PHYSICS · Subjective · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

The fastest possible rate of rotation of a planet is that for which the gravitational force on material at the equator just barely provides the centripetal force needed for rotation. The corresponding shortest period of rotation is T=DπqGρT = \sqrt{\frac{D\pi}{qG\rho}} (where ρ\rho is the uniform density of the planet and pp and qq are integers in lowest forms). The value of (p+q)(p + q) is _____.

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