An object of 3.0-kg mass is located at (0.0 m,8.0 m),and an object of 1.0-kg mass is located at (12 m,0.0 m).You want to add a 4.0-kg object so that the center of mass of the three-object system will be at the origin.What should be the coordinates of the 4.0-kg object?
A)(-3.0 m, -6.0 m)
B)(-12 m, -8.0 m)
C)(3.0 m, 6.0 m)
D)(-6.0 m, -3.0 m)

Question

Quizplus · Accepted Answer

Let the coordinates of the 4.0-kg object be (x,y).
Then, using the formula for center of mass:

x_cm = (m1x1 + m2x2 + m3x3)/(m1 + m2 + m3)
y_cm = (m1y1 + m2y2 + m3y3)/(m1 + m2 + m3)

where m1, m2, m3 are the masses of the objects and (x1,y1), (x2,y2), (x3,y3) are their coordinates.

Substituting the given values, we get:

0 = (3*0 + 1*12 + 4*x)/(3 + 1 + 4)
0 = (3*8 + 1*0 + 4*y)/(3 + 1 + 4)

Simplifying these equations, we get:

12 + 4x = 12
24 + 4y = -12

Solving for x and y, we get:

x = -3
y = -6

Therefore, the coordinates of the 4.0-kg object should be (-3.0 m, -6.0 m).

An Object of 3