The figure shows 4 identical spheres of equal masses m suspended by wires of equal length lo, such that all spheres are almost touching each other. Sphere 1 is released from the horizontal position and all collisions are elastic. We need to find the velocity of sphere 4 just after the collision.

To solve this problem, we can break it down into several steps:

1. Identify the initial conditions:
- All 4 spheres are at rest initially.
- Sphere 1 is released from the horizontal position, so it will start moving downward.

2. Analyze the collision between sphere 1 and sphere 2:
- When sphere 1 collides with sphere 2, it will transfer some of its momentum to sphere 2.
- Due to the conservation of momentum, sphere 1 will reverse its direction and start moving upwards.
- Sphere 2 will acquire some velocity in the downward direction.

3. Analyze the collision between sphere 2 and sphere 3:
- When sphere 2 collides with sphere 3, it will transfer some of its momentum to sphere 3.
- Due to the conservation of momentum, sphere 2 will reverse its direction and start moving upwards.
- Sphere 3 will acquire some velocity in the downward direction.

4. Analyze the collision between sphere 3 and sphere 4:
- When sphere 3 collides with sphere 4, it will transfer some of its momentum to sphere 4.
- Due to the conservation of momentum, sphere 3 will reverse its direction and start moving upwards.
- Sphere 4 will acquire some velocity in the downward direction.

5. Determine the final velocity of sphere 4:
- Since all collisions are elastic, the total kinetic energy of the system is conserved.
- Therefore, we can use the principle of conservation of kinetic energy to determine the final velocity of sphere 4.
- The final kinetic energy of the system will be equal to the initial kinetic energy of sphere 1.
- By equating the initial and final kinetic energies, we can solve for the final velocity of sphere 4.

In conclusion, by considering the conservation of momentum and the conservation of kinetic energy, we can determine the final velocity of sphere 4 just after the collision.