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 $x_{cm} = \frac{\sum m_ix_i}{\sum m_i}$, where $m_i$ and $x_i$ are the masses and positions of the particles, respectively. Given that the center of mass is at the origin (0,0) and one particle is at (3.0 m, 0.0 m) with a mass of 2.0 kg, we can set up the equation $0 = \frac{(2.0\,kg \cdot 3.0\,m) + (3.0\,kg \cdot x)}{2.0\,kg + 3.0\,kg}$. Solving for $x$ gives $x = -2.0\,m$, indicating the 3.0-kg particle is at (-2.0 m, 0.0 m).

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