Four objects are situated along the y axis as follows: a 2.09-kg object is at + 2.97 m, a 2.93-kg object is at + 2.53 m, a 2.57-kg object is at the origin, and a 3.92-kg object is at - 0.496 m. Where is the center of mass of these objects?

x = 0 m

y = 1.02 m

Explanation:

M1 = 2.09 kg

y1 = 2.97 m

M2 = 2.93 kg

y2 = 2.53 m

M3 = 2.57 kg

y3 = 0 m

M4 = 3.92 kg

y5 = - 0.496 m

since all objects are situated on the Y-axis, this means the x coordinate of the center of mass is 0.

To find the y coordinate of the center of mass, we apply the equation below.

sum of moment of the objects about the origin = moment of the total mass of objects about the center of mass

M1. y1 + M2. y2 + M3. y3 + M4. y4 = Mt. Y

(2.09 x 2.97) + (2.93 x 2.53) + (2.57 x 0) + (3.92 x - 0.496) = (2.09 + 2.93 + 2.57 + 3.92) Y

11.68 = 11.51 Y

Y = 11.68 / 11.51 = 1.02 m