Answer:
To find the center of mass of a system with two objects, you can use the formula:
\[ x_{\text{cm}} = \frac{m_1 \cdot x_1 + m_2 \cdot x_2}{m_1 + m_2}. \]
Given that \(m_1 = 1 \, \text{kg}\), \(m_2 = 3 \, \text{kg}\), \(x_1 = 1 \, \text{m}\), and \(x_2 = 5 \, \text{m}\), plug these values into the formula:
\[ x_{\text{cm}} = \frac{(1 \, \text{kg} \cdot 1 \, \text{m}) + (3 \, \text{kg} \cdot 5 \, \text{m})}{1 \, \text{kg} + 3 \, \text{kg}}. \]
Simplify the numerator and denominator:
\[ x_{\text{cm}} = \frac{1 \, \text{kg} \cdot 1 \, \text{m} + 3 \, \text{kg} \cdot 5 \, \text{m}}{4 \, \text{kg}}. \]
\[ x_{\text{cm}} = \frac{1 \, \text{kg} + 15 \, \text{kg}}{4 \, \text{kg}}. \]
\[ x_{\text{cm}} = \frac{16 \, \text{kg}}{4 \, \text{kg}}. \]
\[ x_{\text{cm}} = 4 \, \text{m}. \]
Therefore, the center of mass of these two objects is located at \(x_{\text{cm}} = 4 \, \text{m}\).
