JEE past questions - Centre of Mass

1. Two particles initially at rest move toward eahc other under a mutual force of attraction. At the instant when the speed of A is V and the speed of B is 2 V, then the speed at the centre of mass of the system is

a. zero
b. 1.5 V
c. V
d. 3 V

(1982)

2. State whether the following statement is true or false.

Two particles of mass 1 kg and 3 kg move towards each other under their mutual force of attraction. No other force acts on them. When the relative velocity of approach of the two particles is 2m/s, their centre of mass has a velocity of 0.5 m/s. When the relative velocity of approach becomes 3 m/s, the velocity of the centre of mass is 0.75 m/s.

(1989)