The center of mass (or center of gravity) of a two-particle system is at the origin. One particle is located at (3.0 m, 0.0 m) and has a mass of 2.0 kg. The other particle has a mass of 3.0 kg. What is
The location of the 3.0-kg particle?
A) (3.0 m, 0.0 m)
B) (-2.0 m, 0.0 m)
C) (2.0 m, 0.0 m)
D) (-3.0 m, 0.0 m)

Question

Quizplus · Accepted Answer

The center of mass $x_{cm}$ of a system of particles is given by 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 $i^{th}$ particle, respectively. For a two-particle system with the center of mass at the origin (0,0), we have $0 = \frac{(2.0\,kg \times 3.0\,m) + (3.0\,kg \times x)}{2.0\,kg + 3.0\,kg}$. Solving for $x$ gives $x = -2.0\,m$, indicating the 3.0-kg particle is located at $(-2.0\,m, 0.0\,m)$.

The Center of Mass (Or Center of Gravity) of a Two-Particle