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AP Physics C: Mechanics
2.1 Systems and Center of Mass
IntermediateMCQMathematical14.3k
A horizontal coordinate axis labeled x extends to the right, terminated by an arrowhead. Two vertical tick marks are drawn on the axis, labeled 0 and L. Positioned horizontally above the axis are two identical rectangular rods of length L, both spanning from x = 0 to x = L. The top rod, labeled Rod 1, has uniform light-gray filling across its entire length. The bottom rod, labeled Rod 2, features a smooth grayscale fill that gradually darkens from pure white at x = 0 to dark gray at x = L. Both rods are parallel to the x-axis and to each other. No other labels, lines, text, or axes appear.
Two rods of length \(L\) positioned along the horizontal \(x\)-axis.
Two thin, straight rods, Rod 1 and Rod 2, each of length \(L\), are aligned along the horizontal \(x\)-axis with their left ends at \(x = 0\) and right ends at \(x = L\). Rod 1 has a uniform linear mass density \(\lambda_1(x) = \lambda_0\), while Rod 2 has a non-uniform linear mass density given by \(\lambda_2(x) = Cx\), where \(C\) is a positive constant. What is the ratio \(\dfrac{x_{\text{cm}, 1}}{x_{\text{cm}, 2}}\) of the center-of-mass position of Rod 1 to that of Rod 2?

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