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Question

A mass m1 moving with initial velocity u strikes head on to another mass m2 kept at rest as shown in figure. After collision if |v1|<|u|, then

A
m1>m2
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B
m1<m2
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C
m1=m2
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D
There is no relation between m1 and m2
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Solution

The correct option is B m1<m2

Using momentum conservation,
pinitial=Pfinal
m1u=m2v2m1v1 ...(i)

For elastic collision,
velocity of approach=velocity of separation
u=v2(v1)=v2+v1v2=uv1 ....(ii)

from (i) and (ii)
m1u=m2(uv1)m1v1v1=m2m1m1+m2u

since, we already assumed v1 is in opposite direction of u
v1 must be greater than zero
v1=m2m1m1+m2u>0m2m1>0m2>m1

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