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

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 \[r=\frac{{{m}_{1}}{{x}_{1}}+{{m}_{2}}{{x}_{2}}}{{{m}_{1}}+{{m}_{2}}}\]