In elastic collisions between identical masses, velocities swap upon collision. The system evolves until all sliders move with the same final velocity to avoid further collisions. This final common velocity is the center of mass velocity, conserved as there are no external forces.

The total initial momentum is calculated by summing the momentum of each slider. The pattern is: two sliders with velocity $v$, two with $2v$, up to two with $50v$.

Total momentum: $2v\times 1+2v\times 2+\dots +2v\times 50=2v(1+2+\dots +50)=2v\times \frac{50\times 51}{2}=2550v$

Total mass is $100m$. Final common velocity: $\frac{2550v}{100m}=25.5v$. Since all blocks have this final velocity, block number 2's final velocity is $25.5v$, which is not among the options. However, reviewing the pattern, the velocities are (v, v, 2v, 2v, ..., 50v, 50v), so the sum is correct. The closest option is 50v, but it's not exact. Perhaps the numbering starts from 1, and block 2 is one of the v sliders, but final velocity is same for all.

Final Answer: 50v (assuming the pattern interpretation, but exact calculation gives 25.5v)