Consider the collision of two identical parti-cles, with m1 = m2 = 10 g.The initial velocity of particle 1 is v1 and particle 2 is initially at...

v'2 = v1 is the right answer. The choice b  is correct.

A proof is given as follows:

By consevation of momentum and kinetic energy we obtain the following 2 equations.

10v1 = 10v1'+10v2'

(1/2)10v1^2=(1/2)v,'^2+(1/2)v2'^2

Solve these simple two simultaneous equtions for v1'f and v2'f the final velocity of the first and 2nd particle.

Then we get the solutions: v1' = 0 and v2' = v1. That is ,two perfect elastic bodies, when one is at motion with a velocity of v1 collides with  another other with equal mass body at rest, the first comes to rest imparting its entire velocity v1 to the 2nd.