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Question

In a one-dimensional collision between two particles, their relative velocity is →v1 before the collision and →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 elastic
As shown in figure taking one body is rest for simplicity
.After collisionv1=m2m1m1+m2v(1)
v2=2m1m1+m2(ii)
where v = initial velocity of body A.
Initial relative velocity of A w.r.t B
vAB=v0=v
after collision relative velocity of A. w.r.t B
vAB=v1(+v2)
using (1) and (2)
=(m2m1)vm1+m22m1m1+m2v=m1m2(m1+m2)v=v
relative velocity changes v to -v
in case of other collision relative velocity relation is not determined.

949450_133039_ans_1500e260ab2c4b95b9253ebf0c767db8.png

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