Three masses are located in the x-y plane as follows: a mass of 6 kg is at (0 m,0 m),a mass of 4 kg is at (3 m,0 m),and a mass of 2 kg is at (0 m,3 m).Where is the center of mass (or center of gravity)of the system?
A)(1 m,2 m)
B)(2 m,1 m)
C)(1 m,1 m)
D)(1 m,0.5 m)
E)(0.5 m,1 m)

Question

Quizplus · Accepted Answer

The center of mass $x_{cm}$ and $y_{cm}$ can be calculated using the formulas $x_{cm} = \frac{\sum m_ix_i}{\sum m_i}$ and $y_{cm} = \frac{\sum m_iy_i}{\sum m_i}$, where $m_i$, $x_i$, and $y_i$ are the mass, x-coordinate, and y-coordinate of the ith mass, respectively. For the x-coordinate: $x_{cm} = \frac{(6*0) + (4*3) + (2*0)}{6+4+2} = \frac{12}{12} = 1$ m. For the y-coordinate: $y_{cm} = \frac{(6*0) + (4*0) + (2*3)}{6+4+2} = \frac{6}{12} = 0.5$ m. Therefore, the center of mass is at (1 m, 0.5 m).

Three Masses Are Located in the X-Y Plane as Follows