Physics - Center of Mass Question with Solution | TestHub

The center of mass $x_{com}$ is calculated using the formula $x_{com}=\frac{\sum m_i{x}_i}{\sum m_i}$.

Given masses $1,\frac{1}{2},\frac{1}{4},...$ at positions $1,\frac{1}{2},\frac{1}{4},...$, we have $x_{com}=\frac{1+\frac{1}{4}+\frac{1}{16}+...}{1+\frac{1}{2}+\frac{1}{4}+...}=\frac{\frac{1}{1-\frac{1}{4}}}{\frac{1}{1-\frac{1}{2}}}=\frac{2}{3}$.