Two objects of mass $10 ext{ kg}$ and $20 ext{ kg}$ respectively are connected to the two ends of a rigid ro

Question

Two objects of mass $10	ext{ kg}$ and $20	ext{ kg}$ respectively are connected to the two ends of a rigid rod of length $10	ext{ m}$ with negligible mass. The distance of the center of mass of the system from the $10	ext{ kg}$ mass is

Accepted Answer

Let the $10	ext{ kg}$ mass be at $x_1 = 0$ and the $20	ext{ kg}$ mass be at $x_2 = 10	ext{ m}$. The center of mass $X_{cm} = \frac{m_1x_1 + m_2x_2}{m_1 + m_2} = \frac{10(0) + 20(10)}{10 + 20} = \frac{200}{30} = \frac{20}{3}	ext{ m}$.

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