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, 0.5 m)
B) (2 m, 1 m)
C) (1 m, 1 m)
D) (0.5 m, 1 m)
E) (1 m, 2 m)

Question

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, 0.5 m) 
B)  (2 m, 1 m) 
C)  (1 m, 1 m) 
D)  (0.5 m, 1 m) 
E)  (1 m, 2 m)

Quizplus · Accepted Answer

The center of mass $x_{cm}$ and $y_{cm}$ can be calculated using the formula: $x_{cm} = \frac{\sum m_ix_i}{\sum m_i}$ and $y_{cm} = \frac{\sum m_iy_i}{\sum m_i}$. For $x_{cm}$, we have $\frac{(6*0) + (4*3) + (2*0)}{6+4+2} = \frac{12}{12} = 1$ m. For $y_{cm}$, we have $\frac{(6*0) + (4*0) + (2*3)}{6+4+2} = \frac{6}{12} = 0.5$ m. Therefore, the center of mass is at (1 m, 0.5 m).

Three Masses Are Located in the X-Y Plane