Answer
$\frac{23}{6}(\mathcal{l_o})\approx 3.8 \mathcal{l_o}$.
Work Step by Step
By symmetry, the CM lies on the line connecting all of the centers, the x-axis. Let’s calculate the CM’s coordinate in the x-direction.
The mass of each cube is volume times the density.
$$m_1=\rho (\mathcal{l_o})^3$$
$$m_2=\rho (2\mathcal{l_o})^3$$
$$m_3=\rho (3\mathcal{l_o})^3$$
Locate the CM of each cube.
$$x_1=0.5 \mathcal{l_o}$$
$$x_2=2 \mathcal{l_o}$$
$$x_3=4.5 \mathcal{l_o}$$
Finally, use the above numbers in equation 7–9a to calculate the CM as $\frac{23}{6}(\mathcal{l_o})\approx 3.8 \mathcal{l_o}$.