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Question

# In a one-dimensional collision between two particles, their relative velocity is â†’v1 before the collision and â†’v2 after collision :

A
v1=v2 if the collision is elastic
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B
v1=v2 if the collision is elastic
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C
v2=v1 in all cases
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D
v1=kv2 in all cases, where k1
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Solution

## The correct option is B →v1=−→v2 if the collision is elasticAs shown in figure taking one body is rest for simplicity.After collisionv1=m2−m1m1+m2v→(1)v2=2m1m1+m2→(ii)where v = initial velocity of body A.Initial relative velocity of A w.r.t BvAB=v−0=vafter collision relative velocity of →A. w.r.t →BvAB=−v1−(+v2)using (1) and (2) =−(m2−m1)vm1+m2−2m1m1+m2v=−m1−m2(m1+m2)v=−vrelative velocity changes v to -vin case of other collision relative velocity relation is not determined.

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