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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 :
In a one-dimensional collision between two particles, their relative velocity is →v1 before the collision and →v2 after collision :
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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=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.
As 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 B
vAB=v−0=v
after collision relative velocity of →A. w.r.t →B
vAB=−v1−(+v2)
using (1) and (2)
=−(m2−m1)vm1+m2−2m1m1+m2v=−m1−m2(m1+m2)v=−v
relative velocity changes v to -v
in case of other collision relative velocity relation is not determined.
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