Two particles which are initially at rest, move towards each other under the action of their internal attraction. If their speeds are v and 2v at any instant, then the speed of centre of mass of the system will be :

Two bodies of mass 1 kg and 3 kg have position vectors $$\widehat i + 2\widehat j + \widehat k$$ and $$ - 3\widehat i - 2\widehat j + \widehat k$$, respectively. The center of mass of this system has a position vector :

An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are, 1 kg first part moving with a velocity of 12 m s^$$-$$1 and 2 kg second part moving with a velocity 8 m s^$$-$$1. If the third part flies off with a velocity of 4 m s^$$-$$1, its mass would be :

A particle of mass m is projected with velocity v making an angle of 45^o with the horizontal. When the particle lands on the level ground the magnitude of the change in its momentum will be :