Answer:
The resulting coordinate is [tex](x,y) = (-0.170 \ m , -0.038 \ m )[/tex]
Explanation:
From the question we are told that
The mass of the first dice is [tex]m_1 = 11.10 \ g[/tex]
The mass of the second dice is [tex]m_2 = 15.10 \ g[/tex]
The mass of the third dice is [tex]m_3 = 18.90 \ g[/tex]
The coordinate of the first dice is [tex](x_1, y_1) = (0.3150\ m , -0.4990 \ m )[/tex]
The coordinate of the second dice is [tex](x_2,y_2) = (-0.4050 \ m , 0.4850 \ m )[/tex]
The coordinate of the third dice is [tex](x_3 , y_3) = (-0.1150 \ m , -0.1850\ m )[/tex]
Generally the resulting coordinate of the center of mass of the dice in the x-axis is mathematically evaluated as
[tex]x\ cm = \frac{m_1 * x_1 + m_2 * x_2 + m_3 * x_3}{m_1 + m_2 +m_3 }[/tex]
i.e the summation of the moments about their x-axis divided by the magnitude of their masses
substituting values
[tex]x\ cm = \frac{11.0 * 0.3150 + 15.10 * (-0.4050) + 18.90 * (-0.1150)}{11.100 + 15.10 +18.90 }[/tex]
[tex]x\ cm = -0.170 \ m[/tex]
Generally the resulting coordinate of the center of mass of the dice in the y-axis is mathematically evaluated as
[tex]y\ cm = \frac{m_1 * y_1 + m_2 * y_2 + m_3 * y_3}{m_1 + m_2 +m_3 }[/tex]
[tex]y\ cm = \frac{ 11.10 * (-0.4990) + (15.10) * (0.4850) + (18.90) * (-0.1850)}{ 11.10 + 15.10 +18.90 }[/tex]
[tex]y\ cm = -0.038 \ m[/tex]
Thus the resulting coordinate is [tex](x,y) = (-0.170 \ m , -0.038 \ m )[/tex]
