question_answer

Two identical particles move towards each other with velocity 2v and v respectively. The velocity of centre of mass is   AIEEE  Solved  Paper-2002

A) v 

B)                                           \[v/3\]                    

C)           \[v/2\]   

D)           zero

Correct Answer: C

Solution :

Let mass of each body be m. Their motion is represented as shown in figure.                              The velocity of centre of mass is                 \[{{V}_{CM}}=\frac{{{m}_{1}}{{v}_{1}}+{{m}_{2}}{{v}_{2}}}{{{m}_{1}}+{{m}_{2}}}\]              \[\Rightarrow \]   \[{{V}_{CM}}=\frac{m\times 2v-mv}{m+m}=\frac{v}{2}\]              (the direction              of motion of first particle is taken as positive)    So, velocity of centre of mass of the system is v in the direction of motion of particle having larger speed.