Q. In a carbon monoxide molecule, the carbon and the oxygen atoms are separated by a distance $ 1.12\times {{10}^{-10}}m $ . The distance of the centre of mass, from the carbon atom is :
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Solution:
Key Idea: The cartesian co-ordinate of the centre of mass is $ \frac{\underset{i}{\mathop{\Sigma }}\,{{m}_{i}}{{x}_{i}}}{\Sigma {{m}_{i}}} $ Let the distance of the centre of mass from the carbon atom be r. The mass of carbon, $ {{m}_{1}}=12\text{ }amu $ The mass of oxygen, $ {{m}_{2}}=16amu $
From definition of centre of mass $ {{x}_{cm}}=\frac{{{m}_{1}}{{x}_{1}}+{{m}_{2}}{{x}_{2}}}{{{m}_{1}}+{{m}_{2}}} $ $ =\frac{(12amu)\times 0+(16amu)\times r}{12amu+16amu} $ $ =\frac{16}{28}r=\frac{16}{28}\times 1.12\times {{10}^{-10}}m $ $ =0.64\times {{10}^{-10}}m $
