question_answer

Two identical particles move towards each other with velocity \[2\upsilon \] and \[\upsilon \] respectively. What is the velocity of the centre of mass?

Answer:

                Here \[{{m}_{1}}={{m}_{2}}=m;\]  \[\upsilon =2\upsilon \] and   \[{{\upsilon }_{2}}=-\upsilon \]                 \[\therefore \]  \[{{\upsilon }_{CM}}=\frac{{{m}_{1}}{{\upsilon }_{1}}+{{m}_{2}}{{\upsilon }_{2}}}{m+m}=\frac{m\times 2\upsilon +m(-\upsilon )}{m+m}=\frac{\upsilon }{2}\]