question_answer

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

A)   v       

B)                    \[v/3\]

C)   \[v/2\]             

D)        zero

Correct Answer: C

Solution :

[c] 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.