Correct Answer - Option 3 : 10m/s

__Concept:__

**Collision-**

- The meaning of the term ‘collision’ in our everyday life ‘striking’, in physics it does not necessarily mean one particle striking against another.
- Indeed two particles may not even touch each other and may still be said to collide.
- A collision occurs when two bodies come in direct contact with each other.
- In this event, two or more bodies exert forces on each other in about a relatively short time.
- The collision is in fact a redistribution of the total momentum of the particles

**Types of Collision-**

The law of conservation of momentum holds true in the collision between two masses but,

there may be some collisions in which Kinetic Energy is not conserved.

Depending on energy conservation, Collisions are basically of two types:

**1. Elastic Collision:**

- In the elastic collision total momentum, total energy, and total kinetic energy are conserved.
- Although, the total mechanical energy is not converted into any other form of energy as the forces involved in the short interaction are conserved in nature.

**2. Inelastic Collision: **

- In the inelastic collision, the objects stick to each other or move in the same direction.
- The total kinetic energy of the system containing colliding objects is not conserved but the total momentum and energy are conserved.
- During Inelastic collision, the energy is transformed into other energy forms like heat and light.

__Calculation:__

Mass of the ball, m = 2 kg

Kinetic energy before the collision, K_{i} = 100 J

Let the velocity of the ball after a direct collision with a rigid wall be v.

As the collision is elastic in nature, so the kinetic energy of the ball will remain conserve.

i.e. K_{i} = K_{f}

\(\Rightarrow \frac{1}{2}m{{v}^{2}}=100\)

\(\Rightarrow \frac{1}{2}\centerdot 2\centerdot {{v}^{2}}=100\)

\(\Rightarrow {{v}^{2}}=100\)

\(\Rightarrow v=\sqrt{100}=10\)

\(\therefore v=10m/s\)

Hence, option-**3** is correct