Momentum conservation problem Lets a  plastic ball of mass m which is collided with steel. After collision the ball is coming back with the half initial speed. If the steel doesn't move then how can I interpretate this ?  
Let the initial speed of the ball is  $u_1$ and mass $m_1$ and mass of steel $m_2$  speed of steel before and after collision $0$. 
Therefore we can write according to the conservation of momentum,
$$m_1 u_1 +m_2 u_2 = m_1v_1 +m_2 v_2$$
$$m_1 u_1 = m_1v_1 $$ 
$$ u_1 = v_1 $$ 
I have surmised $u_2 = v_2 = 0$. 

Therefore speed is same then how can the speed of the ball can be
  halved after the collision. Is this because of inelastic collision?

 A: If "the steel" that you're referring to is a fixed object or has a large mass, then the energy lost in the collision goes into increasing the internal thermal energy of the plastic ball and "the steel". This is an inelastic collision and kinetic energy is never conserved in inelastic collisions. Momentum, on the other hand is always conserved in the collision, but as your condition states, "the steel does not move". It means some other particle in the universe is gaining the momentum lost by the particle, or "the steel" moves so slowly that you are unable to measure it, or something else...
A: 
If the steel doesn't move then how can I interpretate this ? 

The interpretation you mentioned is completely wrong.(why?)  

Therefore speed is same then how can the speed of the ball can be halved after the collision. Is this because of inelastic collision? 

No!. Consider the steel is initially at rest and the plastic ball is moving towards it. If the collision is taken place only between these two bodies ( i.e system under consideration is isolated) then even if the collision is inelastic  the velocity of the steel(was at rest before collision) which is been hit after the collision  can not be $0$ even if it were a completely inelastic collision.

The reason why after the collision velocity of steel should not be $0$ is that when the collision takes place both the bodies impart equal and opposite forces on each other.Since a force is acting upon the steel it will increase the velocity from $0$( because initially steel was at rest) to a certain value.  

Then how should we interpret the collision.  

Right interpretation 
Let us suppose the system is isolated then the momentum of the system should remain conserved i.e
   $$ m_1 u_1 +m_2 u_2 = m_1v_1 +m_2 v_2 $$
  $$  \Longrightarrow m_1u_1=m_1v_1 $$   $$\Longrightarrow u_1=v_1 $$  
This result is contrary to the observation($ u_1=-1/2 v_1 $). This implies that our assumption that the system is isolated is wrong.
    A better interpretation is that the system under consideration contains more than two bodies. For example the steel might be placed right behind another object(of same mass as that of steel)  in such a way that when the collision occurs the plastic body impart some force on steel and steel acquires a velocity but suddenly this steel collides with the third body of same mass as that of steel elastically. Now the collision of steel with third body will cause the steel to stop momentarily and the third body will start moving with the speed with which the steel should have been moving. Also since the steel was placed right behind the third body it appears as the steel remains stationary all along.
A: If $m_2 < \infty$ this is impossible. If $m_2 = \infty$ it is possible because $\infty \times 0$ is any number.
