A thin, non-uniform rod of length \(L\) lies along the \(x\)-axis between \(x = 0\) and \(x = L\). The linear mass density of the rod is given by \(\lambda(x) = \alpha x\), where \(\alpha\) is a positive constant. Which of the following expressions gives the position \(x_{\text{cm}}\) of the center of mass of the rod? • Nerd Notes

AP Physics C: Mechanics

2.1 Systems and Center of Mass

BeginnerMCQMathematical18.9k

A horizontal axis labeled x with vertical tick marks at 0 and L. A thin horizontal rectangular rod lies along the x-axis from x = 0 to x = L. The rod has a shading gradient, starting light gray at x = 0 and becoming solid dark gray at x = L. An origin tick mark is labeled 0 at the left end of the rod. No other labels, lines, text, or axes appear. — Non-uniform rod lying along the x-axis.

A thin, non-uniform rod of length \(L\) lies along the \(x\)-axis between \(x = 0\) and \(x = L\). The linear mass density of the rod is given by \(\lambda(x) = \alpha x\), where \(\alpha\) is a positive constant. Which of the following expressions gives the position \(x_{\text{cm}}\) of the center of mass of the rod?

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