During an elastic collision between two bodies, which of the following statements are correct?

I. The initial kinetic energy is equal to the final kinetic energy of the system.

II. The linear momentum is conserved.

III. The kinetic energy during $\Delta \mathrm{t}$ (the collision time) is not conserved.

Three particles of mass $1 \mathrm{~kg}, 2 \mathrm{~kg}$ and 3 kg are placed at the vertices A, B and C respectively of an equilateral triangle ABC of side 1 m . The centre of mass of the system from vertex A (located at origin) is

The centre of mass of an extended body on the surface of the earth and its centre of gravity

A $$1 \mathrm{~kg}$$ ball moving at $$12 \mathrm{~ms}^{-1}$$ collides with a $$2 \mathrm{~kg}$$ ball moving in opposite direction at $$24 \mathrm{~ms}^{-1}$$. If the coefficient of restitution is $$2 / 3$$, then their velocities after the collision are

A ball hits the floor and rebounds after an inelastic collision. In this case

During inelastic collision between two objects, which of the following quantity always remains conserved?

Two particles which are initially at rest move towards each other under the action of their mutual attraction. If their speeds are $$v$$ and $$2 v$$ at any instant, then the speed of centre of mass of the system is