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 :

A shell of mass 200 gm is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. The initial velocity of the shell is :