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Total momentum of a system is said to be conserved in perfectly inelastic collisions also. I have a slight problem trying to comprehend a simple example regarding the same.

If a small mass 'm' , say a ball is thrown at a huge stationary mass 'M' , say a wall. If the collision is perfectly inelastic, both the bodies after collision is expected to follow the same speed. In this case, if the ball gets stuck on the wall the total momentum after collision would be 0. But, since the ball was moving before the collision, it has some finite momentum and hence, the total momentum before collision cannot be zero. What is it that i am missing or misinterpreting ?