The structure of a water molecule is shown in figure(9-E1).Find the distance of the centre of mass of the molecule from the centre of the oxygen atom.

Step 1, Given data and figure

Mass of the oxygen molecule, $m_1=16kg$

$x_1=y_1=0$

Mass of the hydrogen atom, $m_2=1kg$

Step 2, Finding the distance

Now we can write

$x_2=-0.96\times {10}^{-10}sin52{}^{\circ }m$

$y_2=-0.96\times {10}^{-10}cos52{}^{\circ }$

We know

$sin{52}^0=0.788$

$cos{52}^0=0.615$

Now we can write

$m_2=1kg,x_3=0.96\times {10}^{-10}sin{52}^{\circ }m$

$y_3=-0.96\times {10}^{-10}cos{52}^{\circ }$

For finding the center of mass we can write

$x_{cm}=\frac{m_1{x}_1+m_2{x}_2+m_3{x}_3}{m_1+m_2+m_3}$

$=16\times 0+1\times (0.96\times {10}^{-10}sin{52}^{\circ })$

$\frac{+1\times 0.96\times {10}^{-10}sin{52}^{\circ }}{1+1+16}=0$

$y_{cm}=\frac{m_1{y}_1+m_2{y}_2+m_3{y}_3}{m_1+m_2+m_3}$

$=\frac{16\times 0+2\times 0.96\times {10}^{-10}cos{52}^{\circ }}{1+1+16}$

$=\frac{2\times 0.96+{10}^{-10}cos{52}^{\circ }}{18}$

$=6.4\times {10}^{-12}m$