Answer
$$x_{CM}=1.42m$$
$$y_{CM}=-0.25m$$
Work Step by Step
Let the total mass be M. Calculate the mass of the horizontal piece, “1”, and of the vertical piece, “2”. The brace has a fixed thickness, so the mass of each piece is proportional to its area. The width is 0.20 m in each case, so each piece’s mass is proportional to its length.
$$m_{1}=\frac{2.06}{2.06+1.48}M=0.5819M$$
$$m_{2}=\frac{1.48}{2.06+1.48}M=0.4181M$$
Next, calculate the center of mass. The origin is given in the diagram.
$$x_{CM}=\frac{(m_1)(x_1)+ (m_2)(x_2) }{M}$$
$$x_{CM}=\frac{(0.5819M)(1.03m)+ (0.4181M)(1.96m) }{M}=1.42m$$
$$y_{CM}=\frac{(m_1)(y_1)+ (m_2)(y_2) }{M}$$
$$y_{CM}=\frac{(0.5819M)(0.10m)+ (0.4181M)(-0.74m) }{M}=-0.25m$$
