A carbon monoxide molecule consists of a carbon atom bonded to an oxygen atom.The mass of the carbon atom is 75% the mass of the oxygen atom.The carbon atom is located at the origin and the oxygen atom is located at x = d.Where is the center of mass of the carbon monoxide molecule located?
A)0.50d
B)0.57d
C)0.60d
D)0.75d

Question

Quizplus · Accepted Answer

The center of mass $x_{cm}$ of a system can be calculated using the formula $x_{cm} = \frac{\sum m_i x_i}{\sum m_i}$, where $m_i$ and $x_i$ are the mass and position of the ith particle, respectively. For the carbon monoxide molecule, let the mass of the oxygen atom be $m$, then the mass of the carbon atom is $0.75m$. The position of the carbon atom (carbon) is at the origin (0) and the position of the oxygen atom is at $d$. Substituting these values into the formula gives $x_{cm} = \frac{(0.75m \cdot 0) + (m \cdot d)}{0.75m + m} = \frac{md}{1.75m} = \frac{d}{1.75}$, which simplifies to approximately $0.57d$.

A Carbon Monoxide Molecule Consists of a Carbon Atom Bonded