question_answer

In the diagram shown below, \[{{m}_{1}}\]and \[{{m}_{2}}\]are the masses of two particles and \[{{x}_{1}}\]and \[{{x}_{2}}\]are the respective distances from the origin O. The centre of mass of the system is

A)                 \[\frac{{{m}_{1}}{{x}_{2}}+{{m}_{2}}{{x}_{1}}}{{{m}_{1}}+{{m}_{2}}}\]                   

B) \[\frac{{{m}_{1}}+{{x}_{2}}}{2}\]

C)                  \[\frac{{{m}_{1}}+{{m}_{2}}{{x}_{2}}}{{{m}_{1}}+{{m}_{2}}}\]                    

D) \[\frac{{{m}_{1}}{{m}_{2}}+{{x}_{1}}{{x}_{2}}}{{{m}_{1}}+{{m}_{2}}}\]

Correct Answer: C

Solution :

                 The centre of mass of the system \[r=\frac{{{m}_{1}}{{x}_{1}}+{{m}_{2}}{{x}_{2}}}{{{m}_{1}}+{{m}_{2}}}\]