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(D) Let the mass of a wire of length $l$ be $m$.For segment $AB$ (length $l$): Mass $m_1 = m$,Center of mass $\vec{r}_1 = \left( \frac{l}{2}, 0 \right

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$\left( \frac{l}{4}, l \right)$

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(D) Let the mass of a wire of length $l$ be $m$.For segment $AB$ (length $l$): Mass $m_1 = m$,Center of mass $\vec{r}_1 = \left( \frac{l}{2}, 0 \right)$.For segment $BC$ (length $2l$): Mass $m_2 = 2m$,Center of mass $\vec{r}_2 = (0, l)$.For segment $CD$ (length $l$): Mass $m_3 = m$,Center of mass $\vec{r}_3 = \left( \frac{l}{2}, 2l \right)$.The coordinates of the center of mass $(X_{cm}, Y_{cm})$ are given by:$X_{cm} = \frac{m_1 x_1 + m_2 x_2 + m_3 x_3}{m_1 + m_2 + m_3} = \frac{m(\frac{l}{2}) + 2m(0) + m(\frac{l}{2})}{m + 2m + m} = \frac{m(l)}{4m} = \frac{l}{4}$.$Y_{cm} = \frac{m_1 y_1 + m_2 y_2 + m_3 y_3}{m_1 + m_2 + m_3} = \frac{m(0) + 2m(l) + m(2l)}{m + 2m + m} = \frac{4ml}{4m} = l$.Thus,the center of mass is $\left( \frac{l}{4}, l \right)$.

$A$ uniform wire is bent into a $U$ shape with side lengths $l, 2l,$ and $l$. The coordinates of the center of mass of each segment are shown in the figure. The coordinates of the center of mass of the system are:

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