AP Physics C: Mechanics
2.6 Gravitational Force
2.1 Systems and Center of Mass
A hypothetical spherical planet of radius \(R\) and total mass \(M\) has a volume mass density that varies with distance \(r\) from its center according to \(\rho(r) = C r\) for \(r \le R\), where \(C\) is a positive constant, and \(\rho(r) = 0\) for \(r > R\). Which of the following pairs of expressions correctly gives the magnitude of the gravitational field \(g(r)\) inside the planet (\(r \le R\)) and outside the planet (\(r > R\)) in terms of \(G\), \(M\), \(R\), and \(r\)?
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