The value of x = -6.29 m
The center of gravity of the three particles X = m₁x₁ + m₂x₂ + m₃x₃/(m₁ + m₂ + m₃)
Given that the center of gravity is located at the origin, X = 0 m and m₁ = 5.00 kg, m₂ = 4.00 kg , m₃ = 7.00 kg, x₁ = 4.00 m, x₂ = 6.00 m, and x₃ = x m
Substituting the values of the variables into the equation, we have
X = m₁x₁ + m₂x₂ + m₃x₃/(m₁ + m₂ + m₃)
0 = 5.00 kg × 4.00 m + 4.00 kg × 6.00 m + 7.00 kg × x/(5.00 kg + 4.00 kg + 7.00 kg)
0 = 20.00 kgm + 24.00 kgm + 7.00x kgm/16.00 kg
Cross-multiplying, we have
20.00 kgm + 24.00 kgm + 7.00x kgm = 0
44.00 kgm + 7.00x kgm = 0
44.00 kgm = -7.00x kgm
Divide through by -7.00 kg, we have
x = 44.00 kgm/-7.00 kg
x = -6.29 m
So, the value of x = -6.29 m
Learn more about center of gravity here:
https://brainly.com/question/1419972
