Problem 8.37

8.37.

From symmetry, we can see that the $\hat{y}$ component of the center of mass is zero. Looking at the $\hat{x}$ component, we find

$x_{CM} ~=~ \frac{\sum m_{i}x_{i}}{\sum m_{i}}$

$x_{CM} ~=~ \frac{0 + 2 (1.008 u)(.1 nm)(\cos 53{}^{\circ})}{(15.999 + 2(1.008)) u}$

x_CM  =  .00673 nm from the oxygen nucleus.