In a closed system, the loss of momentum of one the gain in momentum of another object.

In a closed system, the loss of momentum of one object  is same as the gain in momentum of another object

according to law of conservation of momentum, total momentum before and after collision in a closed system in absence of any net external force, remains conserved . that is

total momentum before collision = total momentum after collision

P₁ + P₂ = P'₁ + P'₂

where P₁ and P₂ are momentum before collision for object 1 and object 2 respectively.

P'₁ - P₁  = - (P'₂ -  P₂)

so clearly gain in momentum of one object is same as the loss of momentum of other object

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