A person holding a rifle (mass of person and rifle together is 100 kg) stands on a smooth surface and fires 10 shots horizontally, in 5 s. Each bullet has a mass of 10 g with a muzzle velocity of 800 m s^$$-$$1. The final velocity acquired by the person and the average force exerted on the person are :

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 :