Two spheres A and B of masses m₁ and m₂ respectively collide. A is at rest initially and B is moving with velocity v along x-axis. After collision B has a velocity $${v \over 2}$$ in a direction perpendicular to the original direction. The mass A moves after collision in the direction :

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 :