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AP Physics C: Mechanics
2.6 Gravitational Force
2.1 Systems and Center of Mass
AdvancedMCQMathematical25.3k
A horizontal axis labeled with an arrowhead pointing to the right represents the x-axis. A vertical tick mark on the axis is labeled x = -d, where a solid black circular dot representing a point particle of mass m is located. To the right, another vertical tick mark on the axis is labeled x = 0, marking the left end of a narrow horizontal rectangular bar representing a rod of length L. The bar extends along the axis to a vertical tick mark labeled x = L. The interior of the bar has a grayscale gradient shading that is light gray at the left end and becomes progressively darker toward the right end. A horizontal double-headed dimension arrow below the bar spans from x = 0 to x = L and is labeled L. A horizontal double-headed dimension arrow spans from x = -d to x = 0 and is labeled d. No other labels, lines, text, or axes appear.
A point particle of mass \(m\) located along the axis of a non-uniform rod of length \(L\).
A thin, non-uniform rod of length \(L\) and total mass \(M\) lies along the \(x\)-axis between \(x = 0\) and \(x = L\). The linear mass density of the rod varies with position according to \(\lambda(x) = \dfrac{2M}{L^2}x\). A point particle of mass \(m\) is fixed on the \(x\)-axis at position \(x = -d\), where \(d > 0\). Which of the following expressions correctly represents the magnitude of the gravitational force exerted by the rod on the point particle?

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