Consider four point masses located as shown in the sketch. The acceleration due to gravity is the same everywhere. What is the x coordinate of the center of gravity for this system?
A)2.0 m
B)2.7 m
C)3.0 m
D)3.3 m
E)3.8 m

Question

Consider four point masses located as shown in the sketch. The acceleration due to gravity is the same everywhere. What is the x coordinate of the center of gravity for this system? 
A)2.0 m 
B)2.7 m 
C)3.0 m 
D)3.3 m 
E)3.8 m

Quizplus · Accepted Answer

The x-coordinate of the center of gravity can be found using the following formula:

$x_{CG}=\frac{\sum m_i x_i}{\sum m_i}$

where $m_i$ is the mass of the i-th point mass and $x_i$ is its x-coordinate.

Plugging in the values given in the sketch, we get:

$x_{CG}=\frac{(1	ext{ kg})(3	ext{ m})+(2	ext{ kg})(2	ext{ m})+(3	ext{ kg})(1	ext{ m})+(4	ext{ kg})(0	ext{ m})}{1	ext{ kg}+2	ext{ kg}+3	ext{ kg}+4	ext{ kg}}=\frac{13	ext{ m}}{10	ext{ kg}}=1.3	ext{ m}$

Therefore, the x-coordinate of the center of gravity for this system is 3.0 m.

Consider Four Point Masses Located as Shown in the Sketch