Two bodies of masses m1, and m2, moving with velocity u1, and u2, respectively in the same direction collide with each other elastically. Calculate their velocities after the collision. Discuss what happens when
(i) Both the colliding bodies have the same mass.
(ii) One of the bodies is initially at rest.
(iii) A light body collides with a heavy body at rest
(iv) A heavy body collides with a light body at rest

Explanation

To solve the problem of two bodies of masses \( m_1 \) and \( m_2 \) moving with velocities \( u_1 \) and \( u_2 \) respectively, and colliding elastically, we will use the principles of conservation of momentum and the definition of elastic collisions.

### Step 1: Write the equations for conservation of momentum and kinetic energy
For an elastic collision, the following equations hold:

1. **Conservation of Momentum**:
\[
m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2 \tag{1}
...