Two persons of masses 55 kg and 65 kg respectively, are at the opposite ends of a boat. The length of the boat is 3.0 m and weights 100 kg. The 55 kg man walks up to the 65 kg man and sits with him. If the boat is in still water the centre of mass of the system shifts by :

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 :

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 :

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 :