Solving Apparent Paradox: Collision of Two Bodies

[damitr]

Consider collision of two bodies of mass m1 and m2. m2 is at rest whicle m1 moves with velocity v1.
When they collide they sitck together. The question is what is the final velocity V of the two bodies combined.
This apparently simple problem if solved naively leads to an apparent paradox if we solve the problem by
1. conservation of momentum
2. conservation of energy

1.
By conservation of momentum
m1v1+m2v2=(m1+m2)V
since v2=0 we get the final velocity V of the two bodies combined as

V=(m1/(m1+m2))v1

2.
By conservation of energy
(m1v1^2)/2 + (m2v2^2)/2 = ((m1+m2)V^2)/2
here again by substituting v2=0 we get

V= sqrt(m1/(m1+m2))v1
so if we go by two different routes we arrive at two different answers, whereas we should be arriving at the same answer.
So which one is correct?
I know I have applied the concepts very naively, if I am wrong at any point of these derivatiosn please point me.

 

[ZapperZ]

There is no paradox. When there is a 'stick', this is always an inelastic collision. KE is not conserved.

Zz.