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AP Physics C: Mechanics
2.1 Systems and Center of Mass
IntermediateMCQMathematical18.6k
A horizontal axis line representing the x-axis is drawn horizontally across the frame with an arrowhead on the right end pointing to the right. Below the axis, four vertical tick marks are evenly spaced and labeled from left to right as 0, L, 2L, and 3L. A thin horizontal rectangular bar representing a rod of negligible mass rests along the axis, extending from coordinate 0 to 3L. Three solid gray filled circles representing point masses are centered on the rod: the first circle is at x = 0 with diameter approximately three times the rod thickness and is labeled 5m directly above it; the second circle is at x = 2L with diameter slightly larger than the first circle and is labeled 6m directly above it; the third circle is at x = 3L with diameter approximately one-third the first circle and is labeled m directly above it. No other labels, lines, text, or axes appear.
Three spheres of masses \(5m\), \(6m\), and \(m\) attached to a lightweight rod along the \(x\)-axis.
A rigid rod of negligible mass lies along the \(x\)-axis. Three small spheres, labeled 1, 2, and 3, have masses \(5m\), \(6m\), and \(m\), and are fixed to the rod at coordinates \(x = 0\), \(x = 2L\), and \(x = 3L\), respectively.

Three modified configurations are formed by doubling the mass of exactly one sphere while keeping the other two masses unchanged:

Configuration 1: Sphere 1 is doubled to mass \(10m\).
Configuration 2: Sphere 2 is doubled to mass \(12m\).
Configuration 3: Sphere 3 is doubled to mass \(2m\).

Which of the following correctly ranks the \(x\)-coordinate of the center of mass, \(x_{\text{cm}}\), of the rod-sphere system for the three configurations?

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