An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 m s^$$-$$1 and the second part of mass 2 kg moves with 8 m s^$$-$$1 speed. If the third part files off with 4 m s^$$-$$1 speed, then its mass is :

Three masses are placed on the x-axis : 300 g at origin, 500 g at x = 40 cm and 400 g at x = 70cm. The distance of the centre of mass from the orgin is :

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 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 :